Unless you can rely on the Bank of Mum and Dad, you'll probably need to work a bit, as travel is expensive! I personally worked during my gap year up until the June before I started university and then spent a good chunk of the summer travelling around the UK with the money I made (I also made a jump to Paris for a few days in spring! And would have been able to travel more had I not been seeing a girl at the time who was a bit of a money drain
).
The most important thing is to not get carried away just yet and remind yourself that you have to ace your A levels! And then you try to find a job to finance your travels. If you can, ideally try to get a job somewhat related to what you want to study at uni but it's not terribly important and it's absolutely fine if you don't - any job will do and it will make you grow up much more than you'd expect.
In terms of travelling, it's always cheaper to travel within the country you're already in, and the UK has got many beautiful places worth seeing. I could go on and on and on about this so I'll just let you do your own research on what you can visit and do in the UK. I'd recommend getting a 16-25 railcard to travel around the UK by train - it knocks off 1/3 off the prices of trains. Don't know the price these days, but last year it was £30 for one year, £70 for three years. I'd recommend the three years card - it will pay for itself in just a few days of travelling and then you can keep on using it for, well, three years! And if you want to travel on a budget, in the UK or abroad, go to hostels. They're dirt cheap. Not the nicest of places but they do the job. But if you can, I'd definitely recommend going down to mainland Europe and see a few places.
And also, your gap year is the time to do anything you've always wanted to do. I for example picked up the guitar during my gap year