If you are also buying a new property, you need to get that under way as soon as possible so that it does not lag too far behind your sale. Normally, the recommended order of events is that you should find a buyer for your own property first, and then look for a property to buy.
There are a number of good reasons for this. First, you don’t know how long it will take you to sell your property. Second, if you have a purchase already arranged, the stress of worrying whether you will lose the property if you can’t get a sale arranged in time may cause you to lower your price too much or be too easily knocked down by a hard-negotiating buyer.
The best arrangement is to immediately set out to buy a property as soon as you have your home under offer. Figure out well in advance what sort of property you want and where, and get a mortgage lined up in principle.
Check with your solicitors that they have received the contract papers from the sellers’ solicitors promptly, done any necessary searches, been through the papers, and reported to you on any problems which need to be sorted out.