CGT on Transfer 0f Equity

Good Afternoon, I am looking for some advice relating to CGT on Transfer of Equity. My Daughter and her Ex Partner purchased a house in 2005 for £241000. In 2008 her Ex Partner deserted her and in 2010 after paying him £30000 I eventually took on his share of the mortgage and a Transfer of Equity was approved and myself and Daughter became joint owners. I would now like to transfer the Equity to my Daughter and understand I will have to pay CGT, even though I have made no personal gain. Would the Capital gain be calculated using the Property value in 2010 or the original purchase cost? Many thanks for any guidance.

Hi Bill,
As you took ownership in 2010 it is your share of the value at that time.
Thank you.