Apparently the vendor did agree to amend that clause in the contract, so we've gone back to the original terms and conditions. It seems the delay in exchange is actually because HSBC hasn't answered a letter which they received from my solicitor on 6th September, which asks them to confirm that a) they're happy with the house's concrete construction and the remedial works which have added the brick skin and b) they're aware that the sale is of only part of the original property (ie that they know the garden was already sold off to someone else). So yesterday I rang them to chase this up, and point out we were completing in just over a week and they said they'd sort it out as soon as possible and get back to me.
Later yesterday the vendor contacted me to let me know she needs at least a week between exchange and completion. Which means we need these answers from HSBC by *today* - as soon as they say "yes, go ahead" we can exchange. And if we don't get them today then we'll have to move the completion date, because she won't commit to a rental property until we've exchanged and it'll take a week to do the references and so on (apparently). Which is a complete bloody nuisance since we've already committed to moving out, booked a removal firm, allowed our landlord to re-let the property for the end of the week, ordered a fridge to be delivered to the new house and so on.
So today I rang HSBC to try and let them know it's even more urgent than I said yesterday. All the chap I spoke to would say is that someone else is looking into it and will get back to me as soon as possible, and couldn't put me in contact with this person directly or give me any time-scale for how long it's going to take. I don't know if he's even going to pass on the extra urgency, but I was too flustered to make sure.
Originally I was cross at the vendor for not changing the clause, and this turns out to have been unfair, and I was cross at them for not saying originally that they needed longer between exchange and completion than we suggested: I'd have been quite happy to go for longer myself! Now I'm actually cross at HSBC again for adding more unnecessary delays, because they weren't even looking at the question until I rang them yesterday, cross at my solicitor for not allowing enough time for HSBC to be useless in and cross at myself for letting things get into this state. I should never have tried to organise the move for so soon after the original completion date anyway, I was just trying to save a bit of overlap rent, especially since Peter's move date to Cambridge seemed to coincide so well.
Hopefully we'll get it sorted today, if not and we get it sorted tomorrow it's just about still OK, since we weren't going to move out until the day after completion anyway, so could still be out of the house as intended. If not I end up messing my landlord about and messing Peter about or putting our stuff in storage and trying to live in a B&B.
P.S.: thanks for all your kind words on my last post.