Waugh, extremely lonely in flat (6)
I believe the answer is:
evelyn
'waugh' is the definition.
(novelist Evelyn Waugh)
'extremely lonely in flat' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'in' means one lot of letters goes inside another.
'flat' becomes 'even' (level).
'lonely' with its middle removed is 'ly'.
'ly' going into 'even' is 'EVELYN'.
(Other definitions for evelyn that I've seen before include "'Brideshead Revisited' - novel by . . . . . . Waugh" , "& 25 Across Author of 'Decline and Fall'" , "Auberon Waugh's father" , "- Waugh, Eng. novelist" , "- Waugh, English author (Scoop)" .)