Sounds like a right con to me. Every month I make four payments by BACS from my computer. It is credited to the payee almost instantaneously and there are no charges (HSBC).
I had never heard of CHAPS so had to look it up. hc is probably right. BACS has a limit of £10k to individuals and as this is from a solicitor it could be in excess of that, either compensation or result of a property sale.