There are a number of differences in the usage of prepositions and adverbs in the British English and American English. Some of them include:
1. In American English preposition through may mean “up to and including” as in Monday through Friday. In British English preposition to is used instead: Monday to Friday.
2. British sportsmen play in a team, while Americans play on a team (both can play for a particular team).
3. In BrE the word affiliate may be used either with the preposition with or to, in AmE only with is used.
4. The verb check takes no preposition in British English, but it takes the preposition out in American English.
5. The verb stay needs preposition at when in the collocation stay at home in British English and no preposition in American English – stay home.
6. In American English the verb meet takes the preposition with in contrast to British English, where no preposition is necessary - meet with them (AmE) vs. meet them (BrE).
7. The verb fill (when describing the process of completing forms or applications) needs the preposition out in the American English and the preposition in in the British English.
8. In BrE opposite to is an alternative to opposite of. In the AmE, however, opposite of is the only form regularly used (note that opposite as a preposition – opposite the shop – is used both in BrE and AmE).
9. The noun opportunity can be followed either by to-infinitive structure or by a preposition of plus gerund. The latter, however, is rarely if ever used in the AmE and is considered to be Briticism.
10. In Britain people ring or call each other on their phone number, while in America they do it at somebody’s phone number.
11. In BrE the preposition at is usually used when talking about universities or any other educational institutions (She studied foreign languages at university). In AmE, on the other hand, the preposition in can be often used (She studied foreign languages in university).
12. After the verb to write in BrE the preposition to is always used, while in AmE it can be often omitted: I wanted to write to her (BrE). I wanted to write her (AmE).