King, I actually can answer your question! I recently sold an investment property, I only engaged with my solicitor once the property was sale agreed. So I assume, you will need to have the property on the market first.
There are a couple of moving parts for you not withstanding the current 6 week lockdown. If you are now sale agreed, you are probably ~12-16 weeks away from getting the keys? This will vary on the type of property, any requests the sellers are making for vacating the property.
If you put your property on the market now, it depends again on the location, price etc, have you any indication how fast it would sell? For example, a house close to me went sale agreed in October in ~5 days, but there others that have been hanging around. If it takes 6 weeks to go sale agreed, and 12 weeks to go to completio
It is likely you will have a period were you are paying the mortgage on your current property and the new property. I assume this would be the same if you rented, by the time you move out, sort the place out and get a tenant etc.
In my situation, I am budgeting for 3 months of duplicate mortgage payments.