The rules bear only a distant resemblance to other areas of accounting, beyond the use of double-entry book keeping.
The focus is on the separation between client money in client accounts and the firm’s own money in business accounts, as well as keeping proper records of the transactions.
Problem areas include:
mixed receipt (client sends a cheque with both kinds of moneys)
VAT (does solicitors need to pay it for Counsel fees?)
interests in client moneys (does she get any and how much?)
It is also of interest to note that solicitors used to draw and spend money on behalf of their clients for general, non-legal, purposes: but that is no longer permitted.
Complaints against solicitors’ work and bills go first to a body called Legal Ombudsman, which has summary disciplinary powers. Where appropriate the Ombudsman can refer the case to the Solicitors Regulation Authority.
The Court has a supervisory jurisdiction (of medieval origin) to direct enforce a solicitor’s undertaking made by a solicitor (because she is an officer of the Court). But this does not apply to LLPs: see Harcus Sinclair v Your Lawyers LLP [2021] UKSC 32.