I bought some land with one house on it in 1987, and my parents lived in it.  The land and house were transferred to my parents in 1991 with no capital gains tax (CGT).  I built a house in the garden of the original house while still owned and occupied by my parents and the new house has been transferred back to me.  Are there any tax liabilities for either my parents or me?

I am not sure what you mean by 'transferred back to you'. I would have presumed that if you built the house, obviously with your parents’ consent, then the house was yours from 'day 1'. If so the only problem is the land underneath the house. If your parents transfer it to you, then it is quite likely that there is no CGT for them to pay, because most probably they used the land before the building began, and such a transfer is therefore eligible for principal private residence relief. If I am wrong, and the new house belonged to your parents from the beginning, then most probably they will be liable to income tax on its transfer to you.