To give a perspective on this from the other side of the coin....
I have been involved in the building trade for nearly 30 years and in my experience it is the customer who wants to pay cash,
as in: "Oh, and if we pay cash, can we just forget the VAT?"... expecting 20% knocked off. This used to be just on the little jobs, but now people spending tens of thousands on complete re-builds ask.
Well errr no.
For example, on a job of £10,000 plus vat the customer should pay £12,000 [£2000 vat].
That job breaks down to £5000 materials [plus £1000 vat] and £5000 labour [plus £1000 vat] so to just knock off the vat leaves us £1000 out of pocket.
We HAVE to be vat registered, as our turnover is over the threshold, we don't have a choice. Any builder/plumber/ and the like soon hits the threshold when they supply materials. Smaller, "odd job" types might avoid it but we can't.
I can see why they ask, an extra 20% to the government is a hell of a lot, but it is illegal not to charge it and yes, HMRC DO come and check the books and there are huge penalties if you are found out.
Mostly people pay by bank transfer...it's quick and easy. And if they "forget" then it's part of my job to remind them..
After all, Tesco's don't let you off the VAT if you pay cash.
If someone is accepting cash and not giving receipts, I think you need to ask what would happen if something went wrong, have they publicand employers liability insurance, have they a waste transfer licence, are they a bona fide trader at all?