The primary grammatical difference I observe between American and British English is that British writers seem to be allergic to the subjunctive and will go to great (and, to an American eye, often ungrammatical) lengths to avoid using it.
What’s an example of the subjunctive tense in English ?
If I were a rich man ...
More seriously, one reason that the subjunctive is often avoided is that it is rarely distinctive from the indicative. With regular verbs, the only difference is in the third person singular present, "he sing" instead of "he sings". The irregular verb "to be" is the one where the subjunctive is most distinctive, where the bare "be" is the subjunctive in all persons and numbers of the present tense and "were" is the subjunctive in all persons and numbers of the past tense.