As you are buying, you will probably be presented with the invoice from the solicitor on the closing date. They wait until the very end to include all outlay such as searches etc. They usually want the money before they will release keys to you. Have never seen a credit period on a solicitors invoice, but am open to correction.
If you were selling, the solicitor will generally retain their fees from the proceeds of the sale which are given to them by the purchasers solicitor before transferring balance of funds to you.