You would pay a mortgage on 50% and rent on the other 50%, and after 25 years you would own 50% outright and have no more mortgage to pay but would still need to pay the 50% rent. At that point (or perhaps sooner if you get a pay rise/promotion in the next 25 years) you might be able to take out a mortgages for another 25% and own a bit more.
The advantage is that once you retire, and have a smaller income, you won't have to pay the same level of rent as you would if you spent the whole time from now till retirement age renting.
The idea is that you own a percentage of the house so say 50% and the builder retains the other 50%. You then pay your mortgage and a small rent to the builder. it can either stay that way or, if you get a windfall or a good salary increase and can borrow more money then you can increase your mortgage and increase the percentage you own on the property.
I wouldn't go direct to a bank. Go direct to a good independent mortgage advisor as they will have the best deals available to you.
If you are Lothian, Borders, Fife I can recommend someone to you.