"Get a credit card" is NOT the answer. The reason people have a bad (or no) credit score is often because they're new to the country, have just turned 18, have previously fallen into arrears or are just bad with money. Getting a credit card is risky because, if you don't stay on top of your payments, it'll just damage your score even more.
Now, it sounds like I hate credit cards - but I don't, and they do have their benefits. But avoid them if possible because they can be more hassle than they're worth (ie, paying the credit back on-time, cancelling accounts when the interest comes in, moving money in and out of accounts). It's risky borrowing money from anywhere whether it's a payday lender, a bank, a credit card, etc. so use them as a last resort. If you've got your own income then that's amazing. try not to live outside of your means and your credit score will look after (and increase) itself.
time to build a good credit score, but always make sure you pay the people you owe on time and the full amount. I'd stick with paying your phone provider (and any other direct debits you have setup) and avoid getting a credit card.
I'd recommend Noddle to keep track of your credit score and read their FAQ on how to help build it. Unlike Experian. it's free forever so not quite as detailed. but Noddle are owned by CallCredit - one of the biggest Credit Reference Agencies in the UK so they should have the latest information on yourself.
In conclusion, if you already have financial commitments like a mobile phone bill, gym membership, store cards, anything that gets paid monthly by direct debit. your credit score will increase (provided you pay the full-amount on time).
I hope this helps.
PS. I don't work for any of the companies here, but I've been working in the finance sector (more specifically, short-term loans) for 3+ years now.