Continue performing in part of London? (5)
I believe the answer is:
'part of london?' is the definition.
(I've seen this before)
'continue performing' is the wordplay.
'continue' becomes 'act' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'performing' becomes 'on' (as in being on stage).
'in' is the link.
Can you help me to learn more?
(Other definitions for acton that I've seen before include "English statesman" , "Respond in accordance with - London district" , "London area" , "somewhere in London" , "Part of the London borough of Ealing - British historian, d. 1902" .)