Answer: First, get an up-to-date market valuation of the property. You and your parents must decide what share of the house you should buy.
Once you have agreed on the share, consider whether you wish to own the legal title jointly with your parents, or whether they are to continue to hold the legal title, with you having a share of the beneficial interest in the property, which can be evidenced by a declaration of trust.
If you decide on the former, then a transfer document would be needed to transfer to you the agreed share, and that transfer would have to be registered at the Land Registry. You and your parents would become joint registered proprietors. Alternatively, your parents could remain owners of the property and a declaration of trust could be put in place, confirming that they hold the property on trust for you and them, and the terms of that trust. In both cases, a restriction should be placed in the title register.
There may be a capital gains tax liability when your parents sell to you and when you sell in the future, as this is a second home.
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These answers can only be a very brief commentary on the issues raised and should not be relied on as legal advice. No liability is accepted for such reliance. If you have similar issues, you should obtain advice from a solicitor.