Agreed with all the others than there is no legal requirement in the UK to have car insurance simply because you have a licence, or to maintain car insurance whilst you do not have a car.
The only thing not having a car insurance might affect is any no claims bonus entitlement (i.e. a discount on the premium) when you take out car insurance in the future. i.e. if you've had insurance for a number of years previously and haven't made any claims, then that is used for the purposes of calculating your risk profile for the new insurance. I believe that if you do not have car insurance for a period of time (not sure, might be a year or so) that some insurance companies will then make you start from scratch in terms of no claims, meaning that you'd pay a higher premium as you couldn't have the discount. That will depend from insurer to insurer though, as will whether your US driving history can be taken into account.
