When we bought our present property 40 years ago things were a bit different. It was easy to borrow and easy to sell, and we were looking for something specific so we didn't put our house on the market till we'd found it. Then we had a bridging loan to cover the gap in completion dates. But we both exchanged contracts on the same day, couldn't afford to risk losing our buyer.
I suppose it depends why you are moving and what you are looking for, but I would be looking round. Get to know the market in the area you want to buy. If you see something you would like, let the seller know your position, then at least they might come back to you to check how your sale is going if they get a lower offer.