The National Health Service does cover fertility treatments including invitro fertilization (IVF) and ICSI, intra cytoplasmic sperm injection. If you want to have treatment on the NHS you do have to meet certain conditions, and only a definite number of treatment cycles are covered. This number varies throughout the United Kingdom, but no region covers indefinite rounds of treatment. The first step to fertility treatment on the NHS is assessment by your local GP, and a referral to hospital. Referrals are guided by national policy, so you will have to meet certain criteria to be able to get referred. Eligibility criteria depend on whether your in England, Wales, Scotland or Northern Ireland. If you turn out to be eligible, it is likely to you will receive treatment at a hospital. Depending on your area, you could also be treated at a private clinic which has a contract with the NHS this depends on local policy, and it's not something you get to choose.
Keep in mind that the NHS does have waiting lists, so you might have to wait for a while until it's your turn to have fertility treatment. Fertility treatment on the NHS is a great option for those who meet the requirements, but if you are considering applying, you might want to keep in mind that private clinics sometimes have better IVF success rates, and that paying for treatment privately could be more productive.