The only thing that should matter the most to international students like you is their health, even more than their studies. The UK's student healthcare system offering a wide range of health care services, like appointments with doctors, hospital treatment, and dental care, is The National Health Service - NHS.

As an international student studying in the UK, the most critical steps you should take regarding the National Health Service in the UK are:

1. Registering with a local General Practitioner GP Surgery, especially if you have an ongoing health condition, such as asthma, diabetes, epilepsy. Within Great Britain's healthcare system, GPs can diagnose and treat a wide range of health problems. Also, it might be a good idea to check with your university's health centres as they have excellent links with many local medical specialists. 
2. Registering with a dentist as soon as you arrive in the UK might be a good idea as well. Not all dental treatments are free under the NHS, so you might need to be ready to get some prescriptions and dental care. 
3. Resting, eating healthy, and developing overall healthy and positive habits will make it less likely for your to get sick, so taking care of your health, mentally and physically, should be your number one job. Better safe than sorry! 

If you have a disability, long-term health condition, mental health condition, or any learning difficulties, you can apply for a Disabled Students' Allowance (DSA)

Mental healthcare campaigns in the UK are usually held by students' unions of the universities. It's strongly recommended to attend them even if you're not diagnosed with any mental illness; you might encounter a friend who is, so you know how to deal with them, and end the stigma.

Are international students covered by Britain's free healthcare?

EU students should have a European Health Insurance Card - EHIC that entitles them to free NHS treatment. 

Non-EEA students studying courses for less than six months duration are not eligible for free NHS and instead they could get private health insurance.

Non-EEA students studying courses for longer than six months with Tier 4 student visa are required to pay an Immigration Health Surcharge to benefit from the free NHS treatment. Luckily, this surcharge is included as a part of your visa application and costs £150 per year. This will entitle you to access NHS care in the UK at no additional cost, similar to any permanent UK resident.

What about emergencies?

If you got sick during holidays and felt the need to get medical treatment when you're home or not near your university GP, you can contact the nearest one to ask for treatment. You're eligible to receive emergency treatment for up to 14 days; then, you'll need to register as a temporary resident or permanent patient. 

Visiting any NHS urgent treatment centre will provide you with treatment for minor injuries, like cuts and bruises. Bear in mind that they're not to treat life-threatening conditions or long-term ones. You do not need an appointment, and you do not need to be registered.