I tried to sell and buy on the same day 2 years ago. It didn't work due to a delay in transferring the funds between solicitor accounts (done by bank transfer now, not by cheque). My buyer's solicitor refused to release funds until I had moved out, so I couldn't get the funds transferred to buy my new place on the same day. At the last minute I had to arrange weekend storage for all my belongings and find somewhere to stay.
The funds weren't in the vendors' solicitor's account until Monday afternoon, and I was unable to get the keys of my new home until then.
While my buyers weren't cash buyers, the delay wasn't due to mortgage drawdown, it was due to money transfer.
Make sure you have a backup plan in place for you and your belongings.