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Under present law, if a person has over £23,250 in capital (including any property), they must meet their own Nursing Home fees. If a spouse remains residing in the property, the property can NOT be included in the assessment of the party who has entered a Home.
The local authority have the power to reverse any transactions which it believes were made with a view to depriving oneself of assets for the purpose of avoiding care fees. In practice, the closer the transaction occurs to the point at which an individual may need care, the greater the risk of that transaction being set aside by the local authority.
Therefore any proposed gifts of money or property would be seen as your parents deliberately depriving themselves for the purpose of avoiding the payment of care fees.
Hence there is therefore a very large risk that any gift of the property/monies could be reversed by the local authority, whether the property be transferred to the children or is sold and the proceeds given to the children.
The only effective thing your parents could do, if it is indeed practical bearing in mind your parents condition,s is for them both to make Wills, to incorporate a life interest trust in their respective Wills giving their respective shares in the property to a third party (normally the children) subject to right of occupancy for the survivor.This at leasts protects one half of the value of the property, as it would pass to you children on the death of your first parent, and won't be assessed as belonging to your surviving parent, when calculating their capital for Nursing Home fee purposes. This can be done even though your Mother is already in a Home, but their Solicitor will have to make sure that they both have mental capacity before preparing their Wills.
I am sorry this is not the answer you were looking for, but it sets out the legal position.
I hope this assists you.