Normally, it means 'mouth' in UK slang, but I, personally, as born and bred UK resident with a fairly wide knowledge of UK slang, have no idea what it means in this case.

Not care, as I loathe Only Fools and Horses

A quick check with my local expert points to the use of 'Mush' as a term of address "Oi, mush!" to a stranger, and the on-line dictionary confirms this - but there is no evidence anywhere of it being used in the suggested context. Not the first time that writers of Only Fools or Minder get it wrong.