I'd nominate Terence Davies's The Long Day Closes and The Neon Bible.  (I guess some people might question the nationality of the later.  American actors, American source material, American setting--these, perhaps, don't make it the most British of British films.  But it's pretty clear that it's Davies's film (and it was made with British financial backing), so that's good enough for me.)  

Frankly, I'm not too familiar with other British films that have won some acclaim over this same period (e.g. the recent works of, say, Leigh and Greenaway), so I'm not the most authoritative source.  But if there are very many recent British films which are anywhere near as good as the two I've mentioned, I'd be shocked (and a bit ashamed not to have sought them out earlier).  