Spanish has added new words to AmE, but I don't thing that the grammar has had much of an influence. Sometimes AmE has retained older forms while BrE has changed; sometimes the reverse has happened.
Don't forget that, within the main varieties of English, there are dialectical differences, When we talk of 'British English', we are talking of a rather abstract concept in some ways. Some of the regional variations within the United Kingdom and Ireland occasionally use structures that have more in common with standard American English than with standard British English. Just to take one example, many speakers of British English dialects, like speakers of most dialects of American English, never had the shall/will usage that was supposedly standard British English.