Improving old article by fellows in the centre of London (2,3,4)
I believe the answer is:
on the mend
'improving' is the definition.
(on the mend means improving after an illness)
'old article by fellows in the centre of london' is the wordplay.
'old' becomes 'o' (abbreviation).
'article by' becomes 'the' (the definite article. I am not sure about the 'by' bit.).
'fellows' becomes 'men' (fellow can mean a man).
'in the' is an insertion indicator.
'centre of' means to look at the middle letters.
The centre of 'london' is 'nd'.
'the'+'men'='themen'
'themen' placed inside 'nd' is 'nthemend'.
'o'+'nthemend'='ON THE MEND'
Can you help me to learn more?
(Other definitions for on the mend that I've seen before include "Regaining health" , "Informally getting better, improving after illness or accident" , "undergoing recovery?" , "Becoming better in health" , "convalescing" .)