Since I did not have a GP in the UK, I went to my boyfriend's GP. At both visits, the ER and the GP, I was told that I did not need to pay anything.
A&E services are provided free of charge, so there's no need to worry about paying for your A&E visit.
Who does not have to pay for their hospital treatment?
There are some services that are free of charge to everyone:
Emergency treatment given inside an Accident and Emergency (A&E) department, a minor injuries unit or a NHS Walk-in Centre (emergency treatment given after admission to the hospital is not free to all);
http://www.dh.gov.uk/en/Healthcare/Entitlementsandcharges/OverseasVisitors/Browsable/DH_074379However, you would need to pay for your GP visits. Unfortunately, GPs often don't know who has to pay or not, and in my experience, even if you tell them you need to pay, they are reluctant to accept payment. IMO, they probably think they are doing you a favor and being nice; however, I don't think they are aware of the ramifications it could have later on when you apply for visas.
I recommend writing a letter to the GP and asking for a bill. Include your personal details, dates visited, and emphasize clearly that you were not entitled to NHS treatment at the time and should have been billed. State that you are willing to pay the outstanding balance and request a bill (even if the balance is zero). If they do not have billing capabilities (as my surgery claimed), request they send you a written and signed confirmation that they cannot or will not bill you.
Keep a copy of the letter you send them, and any replies they send you. If they send you a bill, pay it and request written confirmation that payment has been made in full and you do not have an outstanding balance.
That way, you have documentation that you have made every attempt to follow the rules and rightly pay for your treatment.