It is very unlikely you will get keys to your new house as you don't yet own it. Most solicitors wouldn't advise their clients to hand over keys before posession.
I moved house this year and asked could I put my furniture in the house the morning of the day of signing, so I could move from my house directly into the new house. Otherwise I would have had to unload into a warehouse for a few hours, and then pack up again and move into new house. Nightmare! Solicitors wouldn't hear of it - wouldn't even allow the estate agent let me in with my furniture and lock up behind me, until I could collect the keys from him later.
What we did was, the people buying my house very kindly agreed to sign their final contracts on a Thursday afternoon and rest of money was handed over, but let me stay in my house until the next afternoon, even though they now owned it. My solicitor got a bank draft first thing in the morning and delivered it to the sellers solicitor. Within an hour I was informed keys were waiting for collection. I was still loading up the first vanload of furniture so it worked out well.
At the same time I had to be prepared to unload into storage or even stay with family for the weekend. Sometimes things don't go to plan.
The only other alternative is to get a bridging loan so you can buy the other house before selling your own, but some of the banks seem reluctant to do this for just a few days. I think it is a lot of paperwork for them, for very little money. Mine refused to do this. Perhaps depends on band you're with.