I am from Greece and I am looking to buy a house in the UK with my girlfriend. My father in law (her father) will pay half of the house price from his account and the rest will be under my name using a mortgage. His money is in a UK account, (it is legal and been through all the money laundering checks to be transferred in the UK). His daughter (my girlfriend) is a UK resident without any income here. In Greece if the dad wants to donate/gift money to his daughter he has to pay tax, so we think the best way is me and her dad to buy the house together (under his name) and then he wants to transfer/donate  it (the house) to his daughter.  In this situation does he have to pay any tax, and if so, how much?

I cannot advise you about Greek tax, but as far as UK tax is concerned, if dad gifts half the house to daughter then this is considered a PET (potentially exempt transfer) for IHT (inheritance tax) purposes. This means that there is no IHT in the UK to pay now and if he lives for seven years after making the gift there is also usually no IHT to pay later. I am making an assumption that dad is not domiciled in the UK. If he does not survive for seven years, and the total of his UK assets i.e. half the house gifted now plus his assets in the UK when he dies (e.g. UK bank accounts) (assuming he makes no other PETs) comes to less than the nil rate band (currently £325,000) then he also has no concern with IHT in the UK.