My buyer has been let down by the person who was going to buy his house. Should I stick with him, or should I remarket. Plus what extra will it cost ?

You won’t be surprised to learn that this is quite a common dilemma, particularly in the current market. With buyers relatively few and far between, do you hang on to the one you’ve already got, who sounds pretty committed, in the hope that he finds another purchaser for his own place quickly, or do you take a chance on finding another one and starting from scratch again?
On the surface, it looks like a tough call. Either way, of course, you could theoretically miss out. You might lose your existing buyer, and get no more takers. After all, you know what they say about a bird in the hand. But then again, there could be a whole flock of other equally suitable birds out there in the bushes, just waiting for the chance to swoop!
In reality, however, this isn’t that much of a problem. Basically, you need to look after number one, so I would advise you to put your property back on the market. You are of course perfectly entitled to do so, since under the English system nothing is legally binding on either party until exchange of contracts. Don’t forget, your buyer would probably have no hesitation in pulling out if he saw something else he preferred.
That said, of course, he certainly needs to be informed of your decision - for three very good reasons (which you can put in your own order of importance). First, your agent is actually legally obliged to do so, in writing. Second, it’s the only decent way to behave. And third, in all probability he will still want to buy your house, so it makes sense to keep him onside, because he might still come up trumps before anyone else.
As for whether remarketing will involve any extra fees, the answer should be a resounding “No.” After all, your agent is probably working on the usual no sale, no fee basis – and hopefully you will have chosen a solicitor who does the same. The only other cost to you so far on the sale of your property is presumably the EPC - and that is valid for 10 years anyway.