I prefer prefer that she drive (subjunctive, more common in American English)
I prefer that she should drive (putative should, more common in British English)
I prefer that she drives (indicative; this would not be correct in
American English but is common in British English)
The committee recommended that she reapply when she had been awarded her PhD. (mandative subjunctive)
The committee recommended that she should reapply when she had been awarded her PhD. (putative should, more common in British English)
John insisted that I have another apple. (subjunctive)
John insisted that I should have another apple. (putative should).
Here's an article on the subject:
"The mandative subjunctive in British English seems to be alive and kicking… Is this due to the influence of American English?"
By Noëlle Serpollet, Lancaster University
Gerd Övergaard argued a decade ago that the mandative subjunctive was becoming more frequent (replacing the putative should and the indicative) in British English, particularly in formal and legal contexts, due to the influence of American English:
Gerd Övergaard, The Mandative Subjunctive in American and British English in the 20th Century. Stockholm, Almqvist & Wiksell International, Acta Universitatis Upsaliensis, Studia AnglisticaUpsaliensia, Vol. 94, 1995.
Quirk, et al., A comprehensive grammar of the English language (London: Longman, 1985) also discuss this issue.