So the long story short is that my husband and I have been renting since we moved in together, in the hopes of saving up enough for a deposit fairly quickly. Then a wedding and 2 children happened, so our savings pot hasn't been growing as much as we'd like! But, we were happy enough renting and hoped to buy in a few years. Until we got a letter from a solicitor a few weeks ago informing us that our home was undergoing repossession proceedings as the landlord hasn't been paying the mortgage 
My amazing in laws gifted us enough money that we were able to bring forward our plans to buy, and after a thousand house viewings in 2 weeks we found a lovely place and had an offer accepted last week. The hearing for the repossession is next Monday and we're going along to ask that our eviction be delayed by 2 months, which is the maximum we can request. Our agent, solicitor and mortgage broker are all aware of the situation we're in and have promised they'll do everything as quickly as possible, but I'm now at panic stations because if the sale doesn't complete within those 2 months, we have nowhere else to go.
Being first time buyers we're already fairly bewildered by the whole process without the added stress of a time constraint! The house we're buying thankfully has no chain and is vacant. So, I'm hoping for advice from people who have recently bought or sold, what do you think the chances are of us getting it done in time?