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Just ask your solicitors to try and negotiate. "Ideally we'd exchange now but complete later because xyz, thoughts" if the response is complete now then you have a decision.
If it's a commercial institution do they really need to push for a fast deal? Maybe there's a couple of grand renegotiation or you rent it off them for 2 months?
Grumpy_Git-
The solicitors tried and got a hard no which contained the word "unacceptable" and said that it was us who'd been pushing for the quick sale (definitely not the case).
The estate agent tried with the buyer and they got a two-week extension which I think we're supposed to be grateful for.
Their story is legitimate, they have someone they want to move in in August and there's work they want (need?) to do first. We knew all of that at the start (apart from when they wanted someone to move in, which we would have said was going to be tight). But their argument - they'd have to find rental accommodation for this person in the meantime - is the same as ours, but we're a young family of key workers trying to relocate, and they're an organisation which owns 400+ properties, including some they let out, so it should be easier for them to compromise than us.
tbc
If they pull out we're really fucked though - we probably wouldn't get the same price again, and we'd probably lose our purchase too.
It's an institution buying our place rather than a family with their heart set on it - that definitely comes with pros (cash buyers, efficiency) but I think the con is that they're probably not too fussed either way.