When you pay your conveyancing, fees depends on whether you are buying, selling or remortgaging. If you are buying a house your solicitor will quire monies up front to cover the cost of searches. Most often you will pay this initial deposit and then the remaining fees will be due upon completion of the house purchase.
If you are selling a house you may have to pay a small upfront amount, however, the majority of the time the fees are payable upon completion of the sale.