Whilst some traders prefer cash for legitimate reasons, ime many do so to enable them to understate their tax liability, be it CT, IT and/or VAT.

If they don't provide you with a reason for the reduction then you could assume they might declare the full amount in due course but if they specifically reference a reason, as the OP's tradesman has done, then it seems likely they don't intend to do that so you must decide whether your social/moral conscience is comfortable facilitating (potential) tax fraud.

I'd concur that the tradesman is taking a risk in being so open about his intentions but the risk sits entirely with them.

As an aside, the tax take for the Exchequer is likely significantly reduced if no direct tax is paid.