and then wonder why I was left staring at a wall in the corner with only a 2 litre bottle of Strongbow for company.

Queen - We Will Rock You

might fit the bill

but 'Pounding' by Doves seems to just have one beat all the way through (with additional crash cymbal from time to time)... or a meringue?

I'm not in a position to check if I'm right or not at the moment but I think "Running Bear" by Johnny Preston may fit the bill.

...by Bruce Hornsby & The Range.

I've pondered this very question on occasion, and do have two suggestions for songs that (very nearly) meet this criterion: Joe Jackson's Steppin' Out is pretty metronomic throughout, and it was only after consciously listening to it for variations that I heard a tiny drum fill just before the fade starts.

Then there's It's Gonna Be A Beautiful Night, from Prince's extraordinary Sign O' The Times. It's a live track, about eight minutes long, with just one "breakdown" moment; otherwise, again, it's metronomic, blissfully simple, and allied to some brilliant bass playing. I love it.

By the Sweet....

Just humming it now.....can't think of much deviation.

"Small Hours", by John Martyn: drum-box.
If I remember rightly, "Da Da Da" had a very unchanging beat.

Is that an example of going from the sublime to the ridiculous, by the way..?

I was struck suddenly by how few drum breaks there are on any of the tracks.

It suits the music, and it's not as if Lindy Morrison was doing Moonesque drum rolls during her stint with the band, but on The Clock I think the only change is a switch from the hi-hat to ride cymbals in the chorus.

Mick Fleetwood is also pretty minimal on the fills during Dreams

I may be mistaken but isn't there a coldplay album (or three) that falls into the category? Far more impressive than just a single song!

The relentless, pounding rhythm of "I'm Waiting for the Man" is the song's greatest asset, but this seemed to be lost on the Velvet Underground members when they reunited in the 90's. The song was ruined with a pathetically orthodox rhythm that made you think their best work was all an accident.

You couldn't move for that rhythm in 1989/90 - it was the beat that went on, and on & on...
Good record.

I think Talk Talk's 'Life's what you make it' fits the criteria with the added bonus of the same piano loop/notes/keys used (sorry not a muso so not sure of descriptions) throughout.

Bright Tomorrow. Or are we not including electronic programmed drums?

Bela Lugosi's Dead by Bauhaus?

by Bill Withers is a pretty minimalist drum track

may have a minor frill but is the same basic fol-de-rol throughout.

"She's Lost Control" similarly.

A lot of Joy Division stuff generally.

from about 74 to 79 or so.
Theres just one Drum Loop all the way through everything.
In fact, I'm sure its the same Drum Loop on just about every Disco record of the period!

Danicing in the Dark.

To Tony Da Vit Live In Tokyo, ok he's a dj, but the drums are pretty relentless for 80 minutes...I think he was the author of the ;Trade sound' - more or less 1/1 all the way through for 12 hours straight.

There is a sentence a never thought I would type. Have to say all the above are pretty lightweight compared to Mr V

Is pretty consistent all the way through, isn't it? Give or take a slight switch in time signature at one point. Don't have a copy to hand to confirm this.