Unlike the US president, the Queen of England is under much more direct threat, even if she were only the titular ruler of the United Kingdom. Clearly so much more than national symbols, the Queen and the royal family represent significant targets for terrorists and not only because they live closer to the people than any President is allowed to.
The Queen needs as much protection as she can get. She is royalty. She is a public figure. She is worth a lot of money. I am sure that there are many forces who plan and plot to either kidnap, kill or commit some other criminal acts towards the Queen. Therefore, no protection is too little.
The Queen, while not actually having a lot of actual political power to run the country, is an important figure in British politics. Having her protected at all times by professional bodyguards who take their jobs very seriously is important. If something were to happen to the Queen, the country would be devastated.
The Queen does not receive too much protection. There are many threats against her life; so the Queen's Guard must always be on alert to protect her. The Queen's Guard never knows if someone is only messing with them, or if that person is actually a threat to the royal family.