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Like others have said including the ever marvellous Tom, I personally would absolutely not exchange until you know at least expected costs and I think anyone asking you to do anything else is whole unreasonable. Is your solicitor advocating you exchange on that basis, because surely that is not ok either, and would your mortgage provider forward the mortgage also not knowing how much these repairs will be?
Def estate agents are there to put pressure on everyone to get the sale completed and them saying the buyer really wants to sell the flat to you is entire BS – neither them or the vendor care who buys it.
I would say you’re on hold with the whole process until the vendor can obtain expected costs (as also you shouldn’t have to run around trying to work these out, it’s not your responsibility or quite frankly your problem, it’s the vendor’s) and then the vendor should pay for them/give you the equivalent funds/reduce the sales price as the flat is still their property atm. There are so many flats, you presumably have a mortgage offer, don’t let them panic you into anything though I appreciate you will have spent some money on legal fees etc to get to this stage but losing that is much the lesser evil than the other possible alternative.
Hold your nerve!!!