There are many well-known differences between British and American English, but these differences won't cause you any serious problems if you work in Britain.
First, there are a few noticeable GRAMMAR differences between British and American English: I'll talk about the two most important ones.
First of all, when Americans make sentences using 'just', 'already' or 'yet', they normally use the past simple tense, while in Britain, we use the present perfect.
So an American, for example, might say:
"I already had lunch." "She didn't arrive yet."
And a British person would say:
"I've already had lunch." - That's "I have already had lunch." Or... "She hasn't arrived yet."
Also, in Britain we often use 'have got' or 'has got' when we talk about possession, while Americans generally just use 'have' or 'has'.
So, for example, in American English we might say: "I have a new car." In British English it's more normal to say: "I've got a new car."
The meaning's the same, there's just a small grammatical difference that you might notice.
There are these and a few other very small differences, but to be honest, these differences almost never make it difficult for us to understand each other.
On the other hand, the differences in VOCABULARY between American English and British English are stronger than the grammatical differences, but again, these very rarely cause serious problems.
A lot of the words which are different are informal or slang words...
For example, I think many Americans would be unfamiliar with the British slang word 'naff', which means 'un-cool' or 'poor-quality'.
On the other hand, a Brit (a British person) might be very confused by a sentence like: "The café is kitty-corner to the pharmacy." This means that the café is diagonally opposite to the pharmacy, but we don't have the word 'kitty-corner' in British English.
Another example would be telling the time... If we want to describe 2:45 in Britain, we might say: "Quarter to three", or 3:15 would be "Quarter past three".
On the other hand, in America, these might be: "Quarter of three" for 2:45, or "Quarter after three" for 3:15.
It's another small difference, but it's one that's not going to cause serious problems - it's quite easy to get used to.
There are also some differences in SPELLING which I should mention. One example of this is the verb 'to practise': In British English, this is spelt with an 'S', so that's P-R-A-C-T-I-S-E. In American English, it's spelt with two 'C's, so in American English it's P-R-A-C-T-I-C-E.
And there are lots of other examples of slight difference of spelling, but about 99% of the time, British and American people can understand each other without any trouble at all. In Britain we watch lots of American films and TV programs, and we listen to lots of American music, so American English is generally very familiar to us.
This is probably not quite so true for an American coming to Britain. Americans, I think, don't watch quite so much British TV or British movies.
I should also point out that regional English can be an important thing to think about. Not everyone in Britain talks like James Bond. There are some regional accents in Britain which you don't hear so often in the movies, and these might be a bit more difficult to get used to.
However, I'd like to finish by saying that many, many Americans live and work in Britain, and they don't have any serious language problems at all.