Is it true that you can receive emergency care in the UK completely free of charge?

Yes it can cause issue with future immigration applications.

Hospital treatment is free to ‘ordinary residents’ of the UK. But if you are visiting the UK – to stay with family, on business, as a tourist, or if you are living here without proper permission – then you are likely to be charged by an NHS hospital for the treatment it gives you. Not paying this charge may have an effect on any future immigration application you make and you risk being turned down

https://www.myhealth.london.nhs.uk/information-for-overseas-visitors

Is the claim true? Will the hospital discharge you without presenting any bill?

For emergency care, it seems true. For any other care you will get billed. Please remember that emergency care is usually considered "what ever it takes to make sure you don't die." So if you get hit by a car, you may well find that emergency care covers the initial stabilization, and the bandaging of that nasty cut so you don't bleed out, but not the casting of bones, or surgeries "preferred" for cosmetic reasons (what I mean is you may get nothing more the stitches, when what you would want, at home, would be something that leaves reconstruction as an option). As a bit of a funny I tend to think of it as, "they will duct tape your insides so they don't fall out, but your going to have to pay for the next roll of tape"

If the claim is true, does it mean that travel insurance is not really needed in the UK?

Travel insurance covers so much more then the actual medical bills. Depending on who is providing coverage, you usually get:

• A trip home
• Help with medical expencies (beyound the inital duct tape)
• Money back for the missing parts of the trip you could not cancel
• Help with lost ID or paper work you need to get home
• A place to stay while you work out other issues that may arise (for example, if you needed to stay longer for treatment)
• Some (limited) legal support, should it be required.

With that said, if you though you needed travel insurance before, then you should still get it now. Emergency care is a very far cry from "all the care I need to make it home"

Would staying in a hospital for free cause issues when applying for future UK visas?

No, but you will not be staying in the hospital for free. It's not accurate, but think of Emergency care as the bare minimum to keep you breathing. So if you had an accident, and you needed emergency care to live, you would get that free. The bandage changes, room and meals, doctor visits, etc. will all cost money. That money would then be billed to you. The free care is more of (again not totally accurate) a way to make sure that the hospitals and surgeries keep you from dieing while they figure out the correct way to bill you, not a way to totally avoid a bill.

If you have an unpaid bill, then yes you could have problems with your next application. And any hospital visit is likely to result in a bill, as you would need and want more then "yep he's breathing" levels of care.