I'm neither UK resident nor a UK citizen. In 2010, I received a property in the UK from my mother as a gift. She is neither UK resident nor a UK citizen and owned that property since 1974. I'm now in need of selling that property. Am I liable to pay capital gains tax (CGT) or any other kind of taxes on the property transfer?

Since you received the property as a gift from your mother in 2010, its value in 2010 is your base cost and therefore your capital gain (i.e. the increase in value from its market value in 2010, until now) is not likely to be that big. But even without that, since you are non-UK resident when selling the property you are not liable to CGT in the UK on the sale. If you were non-UK resident in the tax year you received the property, and you sell the property while non-UK resident, then even if you come to live in the UK afterwards and become UK resident, you will not be liable to any CGT in the UK on this property.