It's your accident insurance company which covers the windscreen, usually only with fully-comprehensive policies. Your policy documents will give you the details of how to do it, including the excess you have to pay and which company you need to use for the repair. It does not usually affect your no-claims discount.
The usual method is just to organise the repair with the designated company and pay them the excess; they claim the rest directly from the insurance company.
Last time I needed a windscreen repair I was surprised to fine they don't have depots anymore; they come to your house. Book the visit online, pay by card at the same time and that's it.