Hiya,
i'm assuming that you are both first time buyers and therefore no stamp duty will be payable. if either of you are not FTB then you will both lose the stamp duty exemption.
the house will be sold to you as full market value of 360k, with 200k consideration and 160k gift from your fiance's grandmother. it may be possible to use the dwellinghouse exemption from capital acquistions tax (gift/inheritance tax) if it is the case that neither of you have any other interest in any property, you have lived there for 3 years and intend to continue living there for another 6 years. it is also required that the reason that you are living with her for the last 3 years is because she is old or infirm (new restriction introducted by finance act 2007). if you use this exemption there will be no gift tax at all on the 160k and it will not be aggregated with future gifts or inheritances.
if this exemption is not open to you - then you will both be taking a gift of 160k from her. your fiance can take approx 52k from her without gift tax and you can take approx 26k from her without gift tax, anything over that amount is taxed at 20%.
an option worth considering would be to give her grandmother a right of residence over the property for her lifetime. this would reduce the value of the house and it would protect her grandmother.
hope that helps