When you refer to "the solicitor" I assume you mean your own solicitor. He must get the money to the sellers solicitor; the sellers solicitors must get the transfer deed and various other documents to your solicitor. Your solicitor must be satisfied with the documents; Searches must be carried out (to ensure that there are no judgments/bankruptcies/undisclosed claims against the title etc.) anf if anything appears on the searches, the sellers solicitor must explain it to the satisfaction of your solicitor.
This process (the "closing" or simply "completion") can in theory take place the same day as the loan cheque arrives with your solicitor. It used to be that solicitors would meet in person to close a sale, and the buyers solicitor would simply endorse the loan cheque over to the sellers solicitor. These days (for various reasons: people using solicitors in different areas, traffic in the larger cities, price competition among solicitors etc.) it is more likely to take place by post, but there is no hard and fast rule. Many solicitors will send money by "same day" credit transfer. It gets there the same day in about 40% of cases (this rises where both the sender and recipient are with the one bank)
So, not to give you a deliberately vague answer, it depends on quite a lot of things. The fact that your cheque is being couriered does suggest that your solicitor is "teed up" for closing the transaction the same day. Why not ask him\her!
Best of luck with it.