Having a good credit history, paying bills on time, not missing payments and not applying for credit regularly will all help give you a good score.
You can manage your bank account in a way which will help to improve your credit score. This means that further down the line you may then be able to successfully take out the product you originally applied for.
Each lender has its own system, but generally, these things can improve your score:
Being in the same job for a long time
Owning your home
Having lived at the same address for a while (more than a year)
Keeping your address records current
Being on the electoral roll
Cancelling unused credit and store cards
Reducing your debts with savings
Paying for insurance up front rather than monthly