As above, talk to the vendor's agent and let them know the situation and get the solicitors talking about timing both transactions together. It is possible to close both on the same day but it requires all parties and their solicitors to be motivated to do so.
That will see you in a chain where you can't complete on your purchase until your current place is sold. IF the house you are looking to purchase is in high demand. The vendor might not want to take on the risks of delays or issues with your sale affecting their plans. When I last moved, we arranged mortgage approval on the basis of renting out the current property so that we could close on the purchase before later selling the other one. With less than 10% of the purchase price you might not have the flexibility to pull that one off though as you do need to be able to service two mortgages for a time.