1. Dear *****, your mother can certainly take your brother to court and get the house put back in her name. Essentially, in law, there is what is known as a resulting trust of the house back in her favour as it was herself and your father who paid the money for the house. Your brother has simply a bare legal title to the house. he is not the true owner. So your mother can seek rectification of the folio in the Land Registry and have the house put back in her name. In law a person, such as your brother is not the true legal owner when he doesn't pay for the house. So, the true legal owner - your mother - can get the house put in her name should she so wish.
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3. You need to get a Power of Attorney from your mother to start legal proceedings on her behalf. IN the actual case, evidence that your mother paid the deposit and the mortgage payments will be sufficient to win the legal case. However, the legal proceedings have to be in the name of your mother, or if she dies, in the name of her estate. So, for this reason, you need ot get a Power of Attorney to start legal proceedings on her behalf.