Hello and welcome to the site. Thank you for your question.
As you have never lived in the property as your main residence, your total gain would would chargeable to CGT.
You state that upon your joint owner's death the property will become 100% yours.
Your cost base for CGT purposes would be 35,000 + the 50% valuation at the time of joint owner's death. In other words, if the property at time of death is valued at say £200,000 then your cost base become (35,000+100,000) = £135,000.
If you were to sell the property for say £200,000, your gain would be (200,000-135,000)=£65,000.You would get gains annual exemption against this gain and the balance would be charged CGT at 18%, 28% or a combination of both depending on your total income in the tax year of sale.
I hope this is helpful and answers your question.
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