There are three complete survivors:
G-AVMN Panzermuseum East, Slagelse, Region Sjælland, Denmark (in overall dark green but appears complete)
https://flic.kr/p/2nqxPFq
G-AVMO Museum of Flight, East Fortune (ex-Cosford)
G-AVMU Duxford
In addition:
G-AVMJ (most of the fuselage, anyway) is at Tresham College, Kettering.
G-AVMZ (forward fuselage) is under cover at the Shannon Aviation Museum here in Ireland.
https://flic.kr/p/dhh3hx
I would recommend a perusal of this website in relation to all things BAC 1-11. This is the UK operators page:
UNITED KINGDOM
The 1-11-510s were commonly enough seen on LHR-DUB services during the late 1970s and early 1980s (probably in the low season, I think). There was also a single series 539GF aircraft (G-BFWN, ex 5B-DAJ) leased from Cyprus Airways from October 1978 to April 1980 and which was a fixture on the evening BA824/5 service during that period, IIRC. The other thing that sticks in my mind is that on MAN-DUB the 1-11s almost invariably cruised at FL120 on the way to DUB and FL110 on the way back - presumably to stay within the levels controlled by Manchester Control, as it then was.