The first thing to note is that movies and TV are not really a guide to how words are used in real life in either British or American English, and certainly the frequency with which they are used on screen has nothing to do with real-life attitudes either. The use of swearing in TV and movies is often a tactical decision to appeal to a particular audience.
In the past, American TV was always more commercial than British TV. The BBC had no advertisements as it was paid with license money, and we also had channels dedicated to "arts" (which became an excuse for more swearing and sex on TV in the name of art!). For this reason, British television was ahead of US TV in breaking taboos and featuring swearing in television shows as they only had the public to please and didn't have to worry about pleasing advertisers. This has definitely changed in recent years with an increase in subscription TV like HBO where people pay up-front for the service and there are no advertisements mid-program. The most popular shows from HBO in recent years have been notably more violent and with stronger language than normal US network television.
In movies though it was probably the opposite. Hollywood had a monopoly on movies and the British film industry was trailing behind. The movie rating system meant American movies could swear if they wanted to, and they did. When many American movies eventually made it to British television during the 80s and 90s they were heavily edited to remove swearing. Also, Britain didn't have anything like the American "PG-13" rating until 1989 when we got a "12" rating. Before that our categories went straight from kids movies to an age-based "15" rating, so "in-between" films from America either got re-edited, or re-rated. These days filmmakers know exactly how many F-bombs they can get away with before a movie goes up a rating and they lose potential cinema viewers, so this dictates how often they use swearing. For example the British "12" rating will allow one f-word, so long as it is not used in a "violent" way, and filmmakers will often make sure they include this so that they can appeal to an adult audience by not appearing as a "kids film" while not barring younger people from seeing it in the cinema.
One extra little bit of trivia about the frequency of swear words on television is that some British television shows made the decision to "invent" their own swear-word so that they could portray the use of coarse language without breaking broadcasting rules of the day. One is the British prison-based sitcom Porridge which used the word "naff" as often as they would expect prisoners to use the f-word. Also, the sitcom Red Dwarf used the word "smeg" frequently because they believed the working-class men they were trying to portray would swear, but the time-slot in which the show was placed meant they could not use actual swear-words so liberally. Again, this just shows that TV shows are controlled in their use of swear words and so are no measure of real-life.
Moving into real-life, there really is no discernable difference between either the meaning or the impact of the 'F' word in Britain or America. Some people, especially younger people, use it quite frequently among their like-minded friends, but it is considered to be "strong", or "coarse", and wouldn't be used in polite company. Everybody knows not to say it at a job interview. I would say that it is used in the same way (by people that choose to) on both sides of the Atlantic.
The British "bloody" is really one of the milder swear words these days and is considered quite old-fashioned and quaint even by the British. I have observed that American TV and movies that cast a British character often use this word in the script more liberally than British people would use it in real life, probably because (a) they think that is what British people say, and (b) because they can get away with it on screen as Americans do not consider it a real swear word. It is more popular with older generations.
Ultimately the thing to remember about any swear-word is that they are not really "rated" based on their meaning; rather their impact and the degree to which they are considered offensive is historical and sometimes beyond explanation. If their meaning dictated the level of offence then "poop" would be as offensive as the 's' word, which it doesn't seem to be. I personally noted on my many visits to the USA that the word "piss" does not seem to be as offensive in the USA as it is in the UK.
To sum up:
- Swear words including the 'F' word are used quite liberally in real-life British English probably about as much as they are in American English, but not by everybody, and only in certain situations. They mostly have the same meanings and the same impact.
- The impact of a swear word is dictated by how the culture perceives it, not by the root-meaning of the word.