Mother's welcoming American publicity for traditional British food (5,4)
I believe the answer is:
mushy peas
'traditional british food' is the definition.
'mushy peas' can be an answer for 'food' (I've seen this before). I'm not certain of the 'traditional british' bit.
'mother's welcoming american publicity' is the wordplay.
'mother's' becomes 'ma's' (ma can mean mother).
'welcoming' means one lot of letters goes inside another (in sense of 'inviting in').
'american' becomes 'us' (abbreviation for United States).
'publicity' becomes 'hype' (hype is a kind of publicity).
'us'+'hype'='ushype'
'mas' enclosing 'ushype' is 'MUSHY PEAS'.
'for' acts as a link.
Can you help me to learn more?
(Other definitions for mushy peas that I've seen before include "Processed vegetables" , "Accompaniment to fish?" , "Pulpy green food" , "Squashed green foodstuff" , "Squidgy green side dish served in a greasy spoon cafe" .)