CGT is not your only concern their would be an additional stamp duty liability as the new home you purchase before selling existing house would mean it would be considered a second property and 3% stand duty would be applied, though you may be able to claim the additional amount back.
Have a read of the link below, hope it helps.
https://www.readysteadysell.co.uk/wh...efore-selling/
Easiest and cleanest way would be to sell before you buy.