I am very sorry indeed for the delay in dealing with the original request. I confirm that the relevant rules and regulations depend upon the court. For example, in the High Court this is governed by Order 7 of the Rules of the Superior Courts which states in the relevant part:
"3. (1) Where a solicitor who has acted for a party in any proceedings has died or become bankrupt or cannot be found or has failed to take out a practising certificate or has been struck off the roll of solicitors or has ceased to act for the party, and the party has not given notice of change of solicitor or notice of intention to act in person in accordance with the provisions of rule 2, any other party to the proceedings or (where the solicitor has ceased to act) the solicitor may, on notice to be served on the first-mentioned party, personally, or by letter addressed to his last-known place of residence, unless the Court otherwise directs, apply to the Court for an order declaring that the solicitor has ceased to be the solicitor acting for the first-mentioned party in the proceedings, and the Court may make an order accordingly."