Can I insure new car under different policy from old car?

You can insure your new car with a different insurance company and still have your old car insured with your current insurer. However you might run into problems with the no claims bonus (NCB) because you either get a full year or NCB or nothing at all. You can only show evidence of a certain number of no claims when you get your renewal letter from your current insurer. This means that when you take out a policy for the new car, you will not have received the NCB entitlement yet and it is advisable not to lie on the details when you're applying for a quote.

If you have like 3 years no claims and in the next 2 weeks you will be getting 4 years NCD, then it might be worth waiting for the entitlement to come through. However if you've already got 10 years worth of no claims, then it will hardly make any difference and you should be fine getting the insurance for the new car.

Note that if you're getting the new car in 2 weeks time, then you can go ahead and put your full no claims bonus (including the one that you'll get on your old car) on the new car because by the time your old policy will elapse, your new one will be starting.