So he's looking to meet you half way on 25% - i.e. 12.5%? Yep pipe up with a 'oh, by the way, you must have forgotten to give me a VAT receipt when I paid you, can I have it now please?' and I'd bet he'll quiet down cos thats 13.5% he'd be losing right there, net result a 1% loss to him. Of course, he may well be an upstanding tradesman who got this wrong and would be paying the VAT either way, but an upstanding tradesman knows that a fixed price is a fixed price so would not be playing these games.
Bottom line is you wouldn't be getting any of this if you hadn't paid him before the job is finished...I've seen so many people in construction change their attitude to a job once they get paid for it: yesterday they were eager to get it done as well as possible, today they feel as if theyre doing you a favour and suddenly have a million and one other jobs to do first.
What exactly has he done so far - has he first fixed the rads, cos it sounds to me like he's out by a mile on his estimates? Did he have to run in the pipes feeding the rads, and what access did he have to do this (i.e. did he have to chase into concrete or were there open ceilings or floorboards he could work with)? Can he name one thing about your house or requirements that was not apparent at quote time which impacted his ability to deliver on schedule? For example, if he said 'jaysus I thought your walls were stud partition but they're all solid concrete blocks so I've had to chase out everything and its really cost me time' I'd be more inclined to meet him half way. However, I expect that yours is a case of the plumber thinking in his head that you've been stupid enough to pay him once when you shouldn't so you might do so again. If he can't name any reasonable unforeseen obstacle that can justify his overrun I'd point out to him that its clearly unacceptable to ask you to pay for his error in judgement, and failing that I'd play the VAT card.