I would be looking for a 10 to 20% discount for paying cash, being a self employed tradesmen I would of course never accept, offer or suggest that this should be encouraged or that HMRC should be taken out of the loop!!! but I believe that it does occasionally happen.
If you could get the person to give you some sort of receipt or written acknowledgement then I think you would be very very lucky as this opens him wide open to be investigated and would probably lead to him being fined for thousands of pounds,as has happened to a number of people I know. However if the work has been good and the installer was recommended and you know their work at other places has been good then its probably worth the risk if you can get something decent off the price. Worst case scenario the money you get as a discount could always be used to pay someone else should there be a minor problem, like an insurance.
If the installers have provided the material they will already have paid for it and either paid the vat or will be added to their account if they have a trade account somewhere so the only vat saved will be on the labour. Assuming they are vat registered.
By them taking cash the only real benefit is for them to avoid paying tax on the income.