If you are buying a new car then you most likely need to switch your insurance over on to it. If you are trading your current car in part exchange or if you are selling it after then you may need to have both cars insured for a period. Most insurance companies will give you 24 hours cover on both to give you plenty of time to collect the new one whilst still being insured on the old one.
When swapping insurance, firstly call your current provider and check what the cost would be to swap. There may be an additional premium to pay and possibly an admin fee too. Once you have a price go online and obtain a quote from a comparison company to see what others may offer you. I often find a price for a few hundred pounds less than your current provider. If you are going to swap insurers check what the cancellation fee is going to be as often this can be in excess of £75 which can make it worth while paying a little extra and staying with your current insurer. Be sure to also check the level of cover you are being offered with the new company is the same as with your current one and that the excess is not a lot more than you would have had to pay.