British and American grammar are nearly identical with slight unremarkable differences.
* In British English a singular noun that represents a group of people/objects is always paired with the plural form of a verb. For example, Americans would say "the class is going on a field trip", whereas Brits say "the class are going on a field trip". However this difference is really more about vocabulary than about syntax. Brits define "class" ( as an example) as a group of individuals and Americans define it as a collective object. The syntax is actually identical; they apply the same rules about agreement between subject and verb and differ on the nature of the noun.
*There's a difference in the use of the present perfect which is really more a matter of semantics than syntax. Americans use simple past where the British insist on the present perfect for things which occurred in the past but have an effect on the present.
*The British use different prepositions with some words ("on line", "in hospital") than Americans do.
In general those differences are slight and not really considerable as a whole ,since the sentence structure is almost the same in both.