You need to ask the insurer but if you move the insurance to the new car on 14th then the insurer may charge you a bit extra if the new car is in a higher group, or they might waive any fee if it's in a lower group. I wouldn't cancel the old policy - you won't get anything back at all.
I think these days of multi-car policies, you don't have to be so squeamish about starting a new policy. The idea was that insurers wanted to know if you had any claims or not. In the old days, your dad and grandad only had one car, so it was a no-brainer that there was only one policy at a time.. but these days we have multi-car households and insurers have rushed to extort a few extra quid from you by saying you can't have "no claims" on more than one car policy at a time.
In my view, you either have claims or you don't... so when they ask "have you got any claims" and you reply "no" then you ought to get the NCD discount, whether you have another policy or not.
You can check their small print in the contract if you want to be sure you're not falling foul of their terms, since it's a business contract at the end of the day but why give that company your business? The more we resist their cobblers, the less they can bend us over, unless of course you like that sort of thing..