That half the average rental in the area thing strikes me as a little odd...
Mortgage payments wont be as much as the local rents so for example:
£100000 with a 80% LTV on a 25 year term
4.0APR = £400 a month
rental in most areas is £550 for a pretty basic place, this will be rent, maintenance and other landlord profit/fees.
with the mortgage, you will never own the place, she will but you are affectively paying half of her mortgage off which she can then profit from...you get nothing, same as if you where renting, correct but at least you can do what you like around the house and its your place and she can just kick you out any time she likes (as can a landlord but notice periods and some laws to protect you).
strikes me as odd and slightly profiteering to charge for half of the mortgage to someone who has no say over the mortgage and house.
just split the bills, not worth the hassle of paying rent or charging rent to a loved one!