The seller of the house pays most of the costs. The house seller pays the Auctioneer / Estate Agent and the Solicitor. They will have to provide a Building Energy Efficiency (BER) Certificate, which is a small cost but is a legal requirement to have when selling your house. The purchaser will have to pay it’s own solicitor, doesn’t have to pay the Auctioneer / Estate Agent but will have to pay stamp duty.
Stamp duty is 1% of the purchase price up to one million or 2% above a million so for most of us is just 1%.