Threads

Other than the Last Train and Threads, the only other one I can think of is When the Wind Blows (wiki link), if you like your dystopian bleakness wrapped in a gentle animated veneer.

1981 TV mini series The day of the triffids https://www.imdb.com/title/tt0081850/mediaviewer/rm737447936

And the 1963 movie before that

28 days later ... almost before 2000

The Changes was decent. Also, after 2000 and more of a comedy but Zomboat was pretty good.

Edit: Also, it's from New Zealand not Britain, but The Quiet Earth is good.

All of the film adaptations of The War of The Worlds are apparently American, but the novel is British, if that'll be adequately British for you.

If have no idea if the movies are any good, but the novel is.

Try The Bed Sitting Room from 1969

https://www.imdb.com/title/tt0064074/

I'm not sure if I'd call it good but it's not terrible.

The original 1970s “Survivors”. Avoid the awful remake.

https://www.imdb.com/title/tt0072572/