Well-liked university in London area (7)
I believe the answer is:
popular
'well-liked' is the definition.
('popular' can be similar in meaning to 'well-liked')
'university in london area' is the wordplay.
'university' becomes 'u'.
'in' means one lot of letters goes inside another.
'london area' becomes 'poplar' (I've seen this before).
'u' placed inside 'poplar' is 'POPULAR'.
(Other definitions for popular that I've seen before include "Well-liked" , "Demotic" , "The people's" , "Widely liked" , "appealing to the public" .)