In a great many housing markets, there are several kinds of mortgages. But basically the fall into two types, fixed and variable (go up and down with then current market rates) -- there's some hybrid loan products and some non ursury types, but this is basically how they break down.
The most popular kind of mortgage is one where the rate is "fixed" or locked at the then current market rate, and it won't change regardless of market forces. The great benefit of these kinds of mortgages is that the repayment terms operate without respect to any inflationary forces or changes in lending markets. Repayment is typically 15, 20 or 30 years.
Historically, and I intend this to mean for something like 99% of history where these types of mortgages have existed, this means that by the end of the loan period, the monetary amount per repayment period (say monthly) is the same, but it's actually cheaper per repayment period in then future real currency. In other words, in 30 years, you're paying for housing at nominal currency values from 30 years prior. Given historic inflation rates, at the end of a typical 30 year loan, this can be around 50% per payment period discount over then future real currency value.
My understanding is that in the U.K., a "fixed rate" mortgage is what we in the U.S. would probably call an "Adjustable Rate Mortgage" or ARM with a fixed 2 year rate (though I believe the closer approximation for an ARM in the U.K. is a discount rate mortgage).
There are also variable rate mortgages, in some markets those are the only types available, in others they exist to cover higher risk borrowers but in others they offer some kind of monetary benefit to the borrower. Depends.
While mortgage rates under such systems can increase, it's not generally normal for them to over decades. For example, in the U.K. over the last 30 years, it's been the general trend for the rates to decrease. (http://www.bankofengland.co.uk/boeapps/iadb/Repo.asp)
Even if the rates do increase at some slow rate, the average of the mortgage payment is still likely to become cheaper over decades than the then future rental price. Following general inflationary trends, rents in most markets have doubled in the past 30 years, while a person who took out a mortgage on a house 30 years ago will be paying much less or will have payed off the property by now and has no specific monthly housing costs.