Yes, you surely can avail the NCB if you change your insurance provider at the time of renewing the policy. All you would need to do is producing a proof of the earned NCB from your current insurance provider. You can produce the original copy of your expiring policy and a certification that you haven’t filed any claim for the (expiring) insurance plan. A renewal notice or a letter stating that you’re entitled to the NCB from your previous insurance provider can be a proof for this.
Soon after the introduction of the Road Traffic Act in 1930, unexpected issues arose when motorists needed to drive a vehicle other than their own in genuine emergency circumstances. Volunteering to move a vehicle, for example, where another motorist had been taken ill or been involved in an accident, could lead to the "assisting" driver being prosecuted for no insurance if the other car's insurance did not cover use by any driver. To alleviate this loophole, an extension to UK Car Insurances was introduced allowing a Policyholder to personally drive any other motor car not belonging to him/her and not hired to him/her under a hire purchase or leasing agreement. This extension of cover, known as "Driving Other Cars" (where it is granted) usually applies to the Policyholder only. The cover provided is for Third Party Risks only and there is absolutely no cover for loss of, or damage to the vehicle being driven. This aspect of UK motor insurance is the only one that purports to cover the driving of a vehicle, not use.