The basis of this is the 2nd Amendment to the US constitution, which gives all citizens the right to bear arms. However, this doesn't stop states regulating it as much as they like, and some do regulate it quite heavily. It is just American culture that happens to be more gun-friendly, and that's the reason for it.
You are wrong about English law. Gun ownership in the UK is perfectly legal, just far more restricted than in most of the USA to the extent that handguns are completely illegal (after the Dunblane shootings), you need to provide a good reason for it and ammunition must be kept locked up. Otherwise how else do the royal family go out shooting wildlife for fun? Or for that matter, anyone else who enjoys the sport.
Now there's a thing - Thomas Hamilton shot up Dunblane Primary School, the government decided it needed to do something to prevent this happening again, and it banned all handguns. As there is no culture in the UK of it being normal to own a handgun, nobody much protested and that got through Parliament. That wouldn't have happened in the USA because of their different culture with regard to guns. (Just out of interest, Andy Murray was at the school at the time, it just wasn't his class that was in the school hall doing PE and so he escaped it. How wonderful that he has put Dunblane in the spotlight for a better reason!)
If you're going to allow other people to possess firearms, then "protection" is a good argument. But what you have in the USA is a powerful gun lobby led by the National Rifle Association, who will argue at length about the 2nd Amendment and the right to bear arms, and that prevents anything more being done about it. And if it's equally difficult for anyone to get their hands on a firearm, then you don't need one for "protection".
Actually if you read the 2nd Amendment, it gives a reason for this right - that it is so the country can have a militia. That made a lot of sense back in the days when the Amendment was made and the USA didn't have a permanent army. England had a similar law 600 years ago - in fact it required all able-bodied men to own a longbow and practise with it every week, in case they were called on to fight France. But now the USA DOES have an army, that reason has gone. Or so some people would argue - the NRA certainly wouldn't!
But the 2nd Amendment is there, it's in the constitution, and the constitution can't be changed unless both houses of Congress decide to change it by a 2/3 majority and 3/4 of the states also agree to change it. It's incredibly difficult for the USA to change its constitution and so it's still there.