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I think there is a conflating here of a breach of conduct rules and professional negligence. For a doctor, professional negligence can have catastrophic consequences such as the death of a patient, which can then result in criminal proceedings (as in this tragic case).
For a solicitor, the consequences of professional negligence are usually financial and there is often no need for the involvement of the SRA. Rather than a complaint and regulatory action, a damages claim by the aggrieved client will be made against the firm. For an employee of the firm there may be in-house disciplinary action, but that would be a private employment law matter.