I am another who recommends having a proper legal agreement between you. Inheritance tax only becomes significant if your total estate is worth over £375,000. If you are widowed, not divorced this can go up to over £600,000.
If you sign over any of the property to your daughter, you will need a very carefully drawn up agreement because if when you need care and as a result of the transfer of your assets to your daughter, any of your care needs to be financed by the Local Authority, they will try and overthrow or override the transfer of your assets to your daughter, saying you did it deliberately to avoid care costs. It will be up to you to prove otherwise - and that is not easy.
This shared house plan is a minefield, there are inheritance tax issues, social care issues, tenancy issues. However, it is a minefield through which a route can be plotted, but you need a competent guide, which in this case is a solicitor who understands these issues.
I would recommend that you go to a large company of solicitors for advice, not a small firm or sole practioner. This is because your situation needs both property, inheritance and social care expertise and you need a company that has experts in all these fields and that is more likely to be found in a large company than a smaller one.