There are some differences in the times that can be used for the same kind of action in British English and in American English. Here as well, one can see the simplification of the tense usage.
1. Thus, in British English when talking about the past action that has an effect on the present situation, Present Perfect is used:
I’ve broken my leg. I can’t visit football practices now.
In American English Present Perfect as well as Past Simple may be used for such a situation:
I’ve broken my leg. I can’t visit football practices now. OR I broke my leg. I can’t visit football practices now (The latter would be considered incorrect in the standard British English).
2. The second main difference also concerns the usage of Present Perfect. In BrE this tense is used in the sentences with the words denoting time reference, such as already, just and yet. In AmE Past Simple can be used, even when the sentence contains the above mentioned words:
I have just washed the dishes. (BrE)
I have just washed / I just washed the dishes. (AmE)
Have you read the book yet? (BrE)
Have you read the book yet? / Did you read the book yet? (AmE)
3. Finally, there is a slight difference in the usage of grammatical constructions with the subjunctive mood. Compare:
The counselor suggested that I visit a professional. (AmE mostly)
The counselor suggested that I should visit / visited a professional. (BrE)
However, there is a tendency to start using the first construction in the British English as well.