Like mentioned it is many things that can improve your credit rating including, long term fixed address, electoral role and good financial accounts. paying off your debts will of course go in your favour because you will reduce your outgoings and therefor give you more "free money" to spend. Having credit on your file and showing regular monthly payments helps to show creditors that you are able to make payments and this will increase your credit score of course. Rather than a student loan, you might be better to have smaller credit arrangements with lower repayments.. ie small credit card, etc.. mobile phone bills can be good too.
When a company want to borrow you large amounts of money, ie mortgage, it is not only your credit file they will want from you. The higher your deposit, of course the better, and they will take into account the value of the property to amount borrowing, and use your house as collateral... so in fact making it much easier to get a mortgage than you might think. They will simply repossess your home if you do not pay! Unlike credit for a car, for example, where it devalues right after purchase!
When purchasing a house.. they will usually have a set calculation from what you earn.. minus usual outgoings, then take a look at your credit file, then they will see if you fit the criteria.. reducing the amount you need to borrow (deposit) in comparison to the value of the house can really have a large influence. Also the housing market in the area you want to purchase and the time of purchase can have an influence.
So overall your credit score would be beneficial to be as high as possible but it will only be a factor in the overall decision to give you a mortgage.
My advice is to pay off your debt asap, use this extra cash once paid off to save save save your deposit.. you will then be in a MUCH better position to purchase a property in 2 or 3 years time.