1. Dear Maurice, I would not let your solicitor's opinion requiring that all four of you agree, stop you from taking legal action. The three remaining siblings should simply go and get a different solicitor. Don't let the solicitor put the dead hand on you taking legal action. This is unprofessional conduct on the part of the solicitor. Ultimately, you cannot account for one of your siblings behaving irrationally and being fearful of an action under the 1975 Act, after time has elapsed.
2. You should essentially seek to have the executors removed after such a long period of inactivity and the failure to administer the estate in such a long time. Additionally, you should seek other relief. However, unless you go forward with legal action, you will not resolve the impasse.
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4. There is the possibility that you can get a new solicitor to work for you on a "no win no fee" basis. Essentially, the agreement by the solicitor to act "no win no fee" has been terminated by the solicitor's refusal to continue to act. So, get a different solicitor who will act for the three of you on the same basis.
5. The current solicitor can charge you for the actual work done. Not the contingency fee. Only for what work, itemised, that he carried out on behalf of the four of you. However, you should negotiate with him. Once he realises that three of you are determined to go to a different solicitor he will likely change his attitude.