If a vehicle is to be "laid up" for whatever reason, a Statutory Off Road Notification (SORN) must be submitted to the DVLA to declare that the vehicle is off the public roads and will not return to them unless the SORN is cancelled by the vehicle's owner. Once a vehicle has been declared 'SORN' then the legal requirement to insure it ceases, although many vehicle owners may desire to maintain cover for loss of or damage to the vehicle while it is off the road. A vehicle that is then to be put back on the road must be subject to a new application for VED and be insured. Part of the VED application requires an electronic check of the MID, in this way the lawful presence of a vehicle on the road for both VED and insurance purposes is reinforced. It follows that the only circumstances in which a vehicle can have no insurance is if it has a valid SORN; was exempted from SORN (as untaxed on or before 31 October 1998 and has had no tax or SORN activity since); is recorded as 'stolen and not recovered' by the Police; is between registered keepers; or is scrapped.
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.