The term undertaking' is defined in the Code as follows:
"'Undertaking' means a statement, given orally or in writing, whether or not it includes the word 'undertake' or 'undertaking', made by or on behalf of you or your firm, in the course of practice, or by you outside the course of practice but as a solicitor or registered European lawyer (REL), to someone who reasonably places reliance on it, that you or your firm will do something or cause something to be done, or refrain from doing something."
The Code requires lawyers to perform all undertakings "within an agreed timescale or within a reasonable amount of time".
The effect of the wording in the Code should not be underestimated. Any person who relies on a statement that a lawyer will do, or refrain from doing, something may claim that a formal solicitor's undertaking has been given. The word undertaking' need not necessarily have been used. Note also that an undertaking given on behalf of a client will normally be enforceable against the firm unless our liability is specifically disclaimed. As we can only undertake matters under our direct control, you must not give undertakings on behalf of clients.
Furthermore, pursuant to the Code:
The Law Society has published a good note on this subject. See https://www.lawsociety.org.uk/topics/regulation/professional-undertakings.