Gifting equity is fine and is a common way for parents to pass on their own family home to their children, it is normally evidenced by a letter from the parents to the lender stating what they are dong and that the gift of equity is a none repayable loan.
I would suggest that there is a further problem to this that you are not aware about.
Abbey (Santander) do accept gifted deposits. I have done many FTB mortgages with them and am currently doing an FTB mortgage wth a gifted deposit with them for a friend of mine and know that this is not an issue as standard.
I would suggest that you contact Santander and ask for a detailed answer to the problem as it may even be a legal problem with the property thats preventing you from buying it. If you have received a formal mortgage offer then it means that Abbey have at some point accepted the gifted deposit as this will be done at underwriting stage which is before the house is even valued and the formal mortgage offer is issued to you and so it must have been acceptable to reach this point. To have the offer retracted means that it has likely either had a head office reveiw and declined on something in the application or there has been a legal aspect of the sale that the solicitor is not happy about and has highlighted to Abbey to change their minds.
I wasn't aware that HSBC did not use gifted deposits (they do not use the professional intermediary market for business) so its not something I would come across easily.
While it has been a blow to your purchase process most other lenders will allow this type of deposit and so if you cannot proceed any further with Abbey then you will have many other choices even from the high street