Same situation, I'm currently on a 3.5k box policy (with a week left on my cool-off) and found a policy that's 2.5k to swap to but is also boxed. Else I'm looking at around the same as you.
I always account for the 20% potential increase (which whilst especially to me, it's unlikely to happen, I'm still the same driver I was when I took lessons; which is ironically more dangerous than being a "regular" driver in some situations), but then I also think about the potential 20% decrease (which no-one ever gets). My situation is also a little different, I make payments on my car - if I didn't the choice would be too obvious, the extra £1k is affordable - screw the box.
If you're making payments on the car the best thing to do is to make a spreadsheet and do a 6 month outlook of outgoings. If you think it looks comfortable after the first 3 months (which are the hardest due to the downpayment on premium) - then you know where you start. If not; in your position; I'd probably just pay the extra, go without the box and actually enjoy my life of not having to flick my eyes at the speedo every 10 seconds.
For the record my car is a 1l lol, I'm extremely jealous your premium must be peanuts in a smaller sized car.