The onus is on the tradesman to pay his tax. I should be able to pay him any way i please, if he then doesnt pay tax he, is in the wrong - not me.
On the few occasions I've had work done for me, there has always been an offer of discount for cash rather than paying the company. It kind of bothers me, but not enough for me to stop doing it.
If he is doing that to avoid tax, then that's his issue - nothing to do with me.
But clearly they aren;t. I have had many a trademan say its £2,000 or if you are paying cash it's £1,600. You would have to be an idiot not to expect that to mean that they are going to account for their tax on what you paid them.