Unfortunately, that's a myth that the Government feed people. The mortgage companies do take in to account your student debt as it is something that will affect how much net income you will have and therefore, the size of the mortgage you can obtain.
Correct but the effect of having the value of your outstanding loan available, in cash, as a deposit will have a far more favourable effect on a mortgage application than having an extra £50-£100 a month net income.
Consider this example. You have a £15k student loan outstanding. You want to buy a £100k house.
Who gets the better mortgage?
Person A, who has just paid off his student loan, has a £15k deposit and earns £1500 net.
Person B, who was about to pay off his loan, but decided this was stupid, has a £30k deposit, and earns £1400 net.
DO NOT PAY IT OFF.
It is NEVER cheaper or better to pay it off. It is NOT conventional debt. It is not 'hanging around your neck'.
Just forget it exists, pretend the deductions are just tax, and live your life.
DO NOT PAY IT OFF.