You'll have the same licence number anyway, and it'll be on the DVLA system by now that you've passed and hold a full licence.
You can sort your insurance online, though if you're looking to get it as cheap as possible then your best bet is to get the cheapest online quote you can, then phone some companies and say you're shopping around and ask if they can beat the quote. Then take that quote to someone else, ask if they can beat it and then go to someone else with that quote. Keep doing that until nobody will budge, then take the cheapest quote you can get. As a first time driver especially, you can save hundreds of pounds on your first year's insurance doing this.