After completion, your conveyancing solicitor will send you an account, covering all their costs and disbursements, as well as the sale price of the house and redemption of the mortgage.
If you are buying and selling at the same time, the conveyancing solicitor can settle up for both transactions at the same time, including paying stamp duty for the house you are buying.
Your conveyancing solicitor will ensure that the change of ownership is registered with the Land Registry.
There is sometimes a small discrepancy and you might even get a small refund.