Part of London well-liked, but not for top people (6)
I believe the answer is:
poplar
'part of london' is the definition.
(district of East London)
'well-liked but not for top people' is the wordplay.
'well liked' becomes 'popular' (I've seen this before).
'but not' is a deletion indicator.
'for top people' becomes 'U' (upper-class, as in U and non-U language).
'popular' with 'u' taken out is 'POPLAR'.
(Other definitions for poplar that I've seen before include "Softwood tree with catkins" , "Tall tree (which may tremble?)" , "Leaves producer" , "Slender tree with quivering leaves" , "Tree, maybe from Lombardy" .)