We are in the middle of it right now, same position as you. Get an "Opinion on Compliance Cert" on your house as well as a BER. Then we followed the exact same steps as you propose but we went Sale Agreed, then 2 weeks later Sale Agreed on new property. Would find it too risky to sell ours and then buy a year later. The rent would be far too high for starters and eat into our funds.
The 10% deposit at signing of contracts is a stumbling block, many would not have that type of cash on demand. If you have manged your money well you would have used excess cash to pay off your mortgage or directed to a pension. To me that advisory is ok when you are a FTB but not for 2nd time buyer, equity should be taken into consideration. In the UK the deposit you receive from your buyer can be used against your deposit.