Early uses

I've found what may be the wellspring of the bastardised form.

The State of the language by Christopher B. Ricks and Leonard Michaels (1990) quotes from a 1988 introduction to the soap opera Eastenders produced by Lionheart Television (the North American distribution arm of the BBC). It reads:
Angie things Den is nothing but aggro. Den thinks Angie is all mouth and no trousers. Sharon thinks they're both berks. Lofty thinks they're all barmy and wishes they'd just belt up - for once.

Google's book search finds just one earlier use, from the London Theatre Review in 1987, in a reference to a comic hero who is all mouth and no trousers.

The bastardised phrase seems to have its roots in the London-based media of the late 1980s. This was the heyday of the Yorkshire sitcom Last of the Summer Wine which, as has been noted, frequently used 'all mouth and trousers', a phrase which might have previously been unfamiliar in many parts of the capital. As that milieu might exemplify the meaning of the original phrase, it seems little wonder the poor dears got confused.

The Google books thing turns up various earlier uses of 'all mouth and trousers', of course. The earliest I can find is in a short story by LP Hartley, collected in 'Two for the River' (1961):
'I wasn't criticizing you,' I said, 'or them.'
'It's not a bad life. Most men are all mouth and trousers— well, I like the trousers best, if you see what I mean.'
'You mean without the trousers.'
'Yes, I suppose I do.'

Earlier examples of either form would be gratefully noted.