Novels set in the Uk from 1940 onwards

A short history of tractors in Ukrainian

I don't know if this might induce snorting, but I've quite enjoyed Jeffrey Archer's Clifton Chronicles, which I initially started just to shut MIL up from going on at me.
The first one is set in the 1920s/30s but the series goes up to the 60s.

The Night Watch/The Little Stranger by Sarah Waters
The Cazalet Chronicles by Elizabeth Jane Howard
both cover 1940s and a bit beyond

More modern settings:

Peter May's Lewis Trilogy are set on Lewis and Harris

Life After Life by Kate Atkinson (goes all over the place date wise though so may be too early) but there are also all her Jackson Brodie books starting with Case Histories and Behind the Scenes at the Museum as well

Paul Torday? He wrote a really wide range of styles of books with all bar Salmon Fishing in the Yemen set in the UK

Maggie O'Farrell's books are all set here

Never Let Me Go by Kashio Ishiguro - slightly dystopian/futuristic UK

A Week in December by Sebastian Faulks

Nick Hornby? All of his though some have been transposed to the States by the movies though they all set out here!

Black Swan Green by David Mitchell (not the comedian)

Alexander McCall Smith's Scotland Street series

Brick Lane by Monica Ali

If you like Margaret Drabble and Margaret Forster (as I do) you may well enjoy Penelope Lively's books.

Barbara Pym

Some of my all-time favourites from around the UK...

Metroland - Julian Barnes
The Buddha of Suburbia - Hanif Kureishi
Brighton Rock - Graham Greene
London Fields - Martin Amis
The Crow Road - Ian Banks
Fat Lad - Glenn Patterson
Submarine - Joe Dunthorne

...although Brighton Rock 1930s (just)

To Bed with Grand Music - Marghanita Laski set during the early years of the second world war. Not read anything by the author before but think that she does write well.

Elizabeth Bowen, Elizabeth Taylor, Dorothy Whipple, Mollie Panter-Downes, you might find the Persephone Books site helpful too.

Billy liar- keith waterhouse?

Not forgetting the great Sylvia Townsend Warner.

The wasp factory- iain banks

I enjoyed The Outcast by Sadie Jones.