First good to hear that you went to uni and got an education. It should pay dividends in years to come.
Being debt free is certainly a good feeling. A lot depends on your short and long term goals.
16k could go a long way to helping you get a deposit for a mortgage, for example. (Then you will have two lots of debt)
But there is good debt and bad debt:
Maxing out a credit card to buy shit you don't need or will never use = BAD DEBT.
Taking out student loans to get a B.A or Masters is a good investment = GOOD DEBT.
Taking out a mortgage to buy property is a good investment = GOOD DEBT.
Just having the money sitting in a bank is not really a good idea. Even today's best tax free ISAs are only paying around 2.75% interest. It would take you 3 years to put the whole 16k into an ISA due to the 5k ceiling per annum. 16k @ 2.75 % per annum is 412.50 (four hundred and twelve pound and 10 shillings) not exactly a princely sum in interest and harldy beating that bastard, inflation. However ISAs are tax free and if/when the economy improves the interest rate could go up to a healthy sum.
Remember: Compound Interest is a Man's Best Friend.
Buy Premium Bonds. Waste of time. The chances of winning as too slim. You would be better off keeping the money in a current account and using the monthly interest to buy Euro Lottery Tickets. Much better chance of winning a million clams.
If you have saved the 16k from earnt income, then you are a good saver and basically should pay off the student loan in one foul swoop and wash your hands of it. You will be able to save up 16k again in the future.
Personally, I would be inclined to find the two birds in your avatar film and present each of them 8 grand to stay the weekend at my house.