Once you have registered with GP you should get an NHS number in the post. If ever you go to hospital then giving them your NHS number on your first visit should be sufficient. When you receive a letter from the hospital it will contain your hospital number! Make a note of that also because it is used for everything to do with that hospital and is good to have when calling them.
You are a British citizen and therefore under the Immigration Act 2014, you (and those with a valid ILR) are allowed to use the NHS bill free, as long as you are residing in the UK.
jcotter is on a temporary visa.
From my link above-
Why you need a BRP
You can use your BRP to confirm your:
identity
right to study or work in the UK
right to any public services or benefits you’re entitled toWhen the NHS part of that Act started from 6 April 2015, the instructions to the NHS staff from the government, is for hospital staff is to check their BRP and the NHS SPINE system, in case their BRP has been curtailed and they need to be billed. Also under that Act: the NHS Trust keeps the money if they are billed, to avoid using their own budget; 50% added if there is no insurance to pay, which the hospital can keep too; the hospital can ask for payment up front and refuse treatment if they don't pay, if it is not life saving treatment, but these still get billed: the NHS Trust can be fined if they didn't bill.
At the same time as the Immigration Act started for the NHS from 6 April 2015-
-British citizens who have a full UK state pension but live abroad, can no longer use the NHS bill free when they visit. These now need insurance to pay or they will have 50% added to the bill.
-the UK ended paying the medical bills of the British citizens retirees living in an EEA country, unless they are in receipt of a UK state pension (have contributed to the UK). These then had to buy their own health insurance. The government stating that just having British citizenship, does not mean the UK will provide them with free medical care if they havent contributed to the UK. The UK will pay for the non-Brits in receipt of a UK state pension as these have been working and contributing to the UK.
The government then ended the piggy backing of a UK state pension off a partner.
Now, only their own contributions to the UK will go towards a UK state pension, or a relavant UK benefit that gives NIC Credits e.g. Child Benefit if the claimant is not paying NICs. Under current rules, it is at least 10 years of NICs before state retirement age, to have a (part) UK state pension.