the buyer of your house will serve a 28 day notice on you to get out. i don't think there's anything you can do - friends of mine had to move back in with their parents, i'm sure this type of thing happens all the time.
Has your purchase definitely fallen through?
Are you definitely legally bound to sell yours regardless?
Is there any chance that you can convince/incentivise your buyer to pull out if necessary?
If not then I guess you need to start looking for an alternative purchase yourselves and maybe prepare for having to rent (or share with relatives/friends etc. if possible) in the near future while you sort yourselves out.
I bought a property as an investment a few years ago and that's exactly what the sellers asked me. I was delighted to oblige and was very flexible about when they could leave - they simply explained their predicament to me. I'm sure the buyer would be happy to be flexible with you if you explain the situation.
Usually a solicitor would ensure that where there is a back to back transaction that both contracts are signed at the same time. This is on the face of it, similar to closing a contract without the bank facilities agreed.
Someone either agreed this or solicitor fouled up.