Hi,
If this property was your dad's main residence, then he would be able to claim Private Residence Relief to offset any gain. You can see guidance here:
HS283 Private Residence Relief (2024)
There is also a capital gains tax calculator to help work out if there is a gain here:
Tax when you sell property
As there is a connection between your dad and yourself, he will need to use the market value of the asset to obtain a disposal value for working out his gain. You can see more information here:
CG14530 - Consideration for disposal: market value rule
If you dispose of the property at some point in the future, you would need to work out how much you paid for your 50% and the market value of the 50% gifted by your dad. This will give you, your 100% acquistion cost, which is deducted from the disposal value to work out if there is a gain. Again, Private Residence Relief may apply.
Thank you.