A month ago I would have listed two.
1. The Distractions - Nobody's Perfect (A magnificent album that hasn't aged at all - it's hard to believe that it's over 30 years old - it still get regular plays in my house)
2. Hal - Hal (fabulous power pop from 2005 - The good news is that they've reformed - the first 3 tracks released so far hint that they haven't lost it so I'm very much looking forward to the new album)

One perfect La's album...

I would nominate Plainsongs 'In search of Amelia Earhardt'. They recorded a follow up that never got released. Years later they brought out another album but it was by a totally different line up. I contendtherefore that the original Plainsong only released one album and that it was and is rather wonderful.

Eric Matthews and Richard Davies collaboration produced one glorious album:

is record companies – if said album sold by the bucketload – will rummage around in skips and archives to cobble together anything they can flog to a willing public. So, The Sex Pistols are really a one-album wonder, but there are several Sex Pistols albums doing the rounds.

Jeff Buckley would have been a one-album wonder on account of his untimely death, but there was enough unfinished stuff to release several albums.

by Eg and Alice gets my vote whenever this topic comes up. An album as melodic and as musically diverse as this deserved better. But despite being hailed as one of the albums of 1991 by many music critics, including Q magazine, it failed to chart.

Much of it was recorded in a kitchen in Camden, apparently.

One album, one single. Not even reissued on CD.

The shape of things to come - I remember it on TOTP 1979, what a fantastic racket, great record.

Spend forever recording their debut double album "Everything Picture", then promptly split up. It's way too long but it's a magnificent mess.

Who, you may ask? Mersey-Beat band who waited until 1969 to record an album for EMI and then promptly broke up. Not really psych, certainly not prog, but well played, post-mod pop. It was reissued way back in the 1980s (see below) which is when I first heard it.
(your 'strictly one album only' rule is exacting, Mr Page)

Rosie Vela – Zazu

Released one Dantastic (geddit?) album and that was it.

Session bassman extraordinaire Herbie Flowers made an album called "Plant Life" in 1975, produced by Brian (B.A.) Robertson. Despite never having appeared on CD* it has long been my favourite album of all time.

While a further LP, "A Little Potty", was put out, it wasn't a "proper" LP, being a compilation of his EMI singles. I'm not sure if Flowers counts here due to:
a) his later chart involvement as part of Sky;
b) his extensive chart involvement as a session player.

*I made enquiries at Universal Music to see if the tracks could be licensed. The answer was yes, but they said they "didn't know" [sic] where the master tapes were located (this was five years ago.) From other dealings both directly with Universal, and knowing other people with the same story to tell, it seems that Universal managed to misfile a large part of the former Philips UK tape library. Certainly when an orchestral Musical Director I work with recently wanted to license and reissue one of his out-of-print titles now controlled by Universal Music, he ended up getting a copy of the (fortunately digital) recording from me - the original editor - as Universal couldn't find it. The original CD was issued less than ten years ago.

Sorry, I seem to have wandered off-topic a bit.

is Jakob Hellman.
Released the album ...Och Stora Havet in 1988 (I think) to rave reviews and sold a ton of records.
It ends up top three (and often reach top spot) every time any voting goes on for best ever Swedish album.
But he never released another one.
Here's the biggest hit, Vara Vänner ( Be Friends ):

Mary Margaret O'Hara's 'Miss America'...

and I really miss the Eighteenth Day of May. (If you haven't come across them but like, say Espers or Trembling Bells, please track down their album!)

They produced an album for Island in the early 70s. There is supposed to be a second one in the can. Its pretty good. I had a girlfriend who really liked it a lot. Some years later I was in a record shop somewhere in the Midlands, (I really can't remember where, but it wouldn't have been too far from Coventry as I was with a mate who lived there) where I came across a whole rack of SPS albums. I doubt that I paid more than £1. Bargain.

They foundered on Wayne Perkins being in huge demand as a session player

Neither Washington Nor Moscow

Keep by Syndicate - a glorious glam racket from 1989 . On EMI , great single , Baby's Gone , got some radio . Clearly love Bowie , Mott , Roxy , T.Rex etc and there's at least two images of the Dame on the sleeve ... there's even a track called The Word on it...What's not to like ?

S*M*A*S*H and their album Self Abused. Gets a regular airing on the Pod. I loved em, the energy, the thrashy sound, the Clash posing, even the simplistic almost naive lyrics. Musically they're sound almost Pixies-ish - check out the bass. Self Abused is possibly one of my favourite punk albums of all time strangely.

And These Animal Men, who are more New Wave, very Mod-Glam and very energetic. I mean just look at them, that Mod meets Clockwork Orange thing that early Manics and Boys Wonder played with too. They did more than one album, but Come On Join The High Society was the only one I bought. And it's a cracker, like I said, all Mod-Glam sharp sharp songs - like The Clash meets The Spiders From Mars.

And they went on to become Mo' Solid Gold who did one good album Brand New Testament, which features an absolutely cracking single Prince Of The New Wave, which unfortunately isn't on Youtube, but is fantastic.

Fire Engines - Lubricate Your Living Room

The Scars - Author! Author!

Girls At Our Best - Pleasure

Mo-Dettes - The Story So Far

Maurice Deebank (Felt) - Inner Thought Zone

Josef K - The Only Fun In Town

Shop Assistants - Same

Delta 5 - See The Whirl

Young Marble Giants - Colossal Youth

Probably doesn't count because they were a Supergroup but it's still a fine album.

The La's still have to remain the ultimate Single Album group.

Only released one proper album and it's one of the greatest of all time (Odessey and Oracle).

A familiar story, one cracking album (This is Hazelville). Brilliant gigs, started to get a following, singles charted but nothing went top 10. Recorded 2nd album, dropped by EMI. Album shelved. Band split in 2009. Bugger.

Feeling Strangely Fine was a superb album, then I believe they followed it up with a song that had something to do with Chemistry. But as a stand alone record, Feeling Strangely Fine was awfully good.

Matthew Jay's album Draw is great. It was his only one, he died a couple of years later. Very sad. I still play it a lot, here's one of the highlights:

one early 90s album, Road to Freedom, then nothing.

Sort of jazzy Brit-soul with strong melodies. Still one of my favourites.

I bought 'In On The Off Beat' in '83 or '84 because I loved 'This Town.' I've never seen anything else by them.

X-Ray Spex, Germ Free Adolescents. Poly was a one-off.

Ian Dury's "New Boots and Panties!" was the only complete quality album he produced, and otherwise he was, in truth, a singles artist (good to great singles, mind). Seriously; "Do It Yourself" was over- and under-worked at the same time, "Laughter" a bit of a car crash, and subsequently he produced good tracks, but weak albums.

by David (Baerwald) and David (Ricketts). A great 80s / Hollywood album, by turns cynical and yearning. Suitably abrasive production from Davitt Sigerson. David Ricketts went on to work with Toni Childs - almost a one-off with "Union" herself - and David Baerwald's solo albums are worth investigating. "Triage" from 1993 is almost a 90s sequel to "Boom Town"

The sublime, 'Electribal Memories' from 1990, even written up in the NME as the 'best debut album since Roxy Music'. That's probably pushing it, but it's closer than you'd think.

Singer Billie Ray Martin has a respectable enough solo career but nothing's quite come close to 'You're Walking', 'Tell Me When The Fever Ended' and especially 'Talking With Myself' - a genuine contender for best 12" single ever.

"Pickled eggs & sherbert" - 97 /98 time. (I know its a bit of a cop out, as they were not a band as such, more of a Sheffield collective) & it was a compilation album.

Nonetheless,I thought it was superb.

...has done only one album so far, produced by R.Hawley (lots of baritone guitar and stuff)and it is very good indeed.

of the tracks, i recommend checking out 'People used to dream about the future' and this one:

A fantastic trip hoppy band from Bristol in the mid 90's.They did a fantastic one off album called 'Radar'. I think there's a Portishead connection.

Had an album called Fear of success.
I first heard him on the credits of the film One Night At McCool's
Great classy hooky pop, then nothing.
There's only a couple of clips on YouTube.
Anyone else heard of him or is it just me?

A bit of a cheat as it's a collaboration between two established musicians (from Portishead and Talk Talk) but Out of Season is a great album.

Holborne was an Elizabethan composer of consort music, and he only really made one (concisely titled) album:

"Pavans, Galliards, Almains and other short Aeirs, both grave and light, in five parts, for Viols, Violins, recorders or other Musicall Winde Instruments" - released in 1599.

All the Holborne albums you ever see on Amazon, etc. are basically just recyclings of the above collection. The most common title it goes under is "The Teares of the Muses" (he clearly wasn't much of a proof-reader - surely there shouldn't be an e between the r and the s in "Teares"?).

Anyway, the main thing to say about Holborne's one album is that it is absolutely exquisite and wonderful, and if you haven't heard it, you should. You really should.