A high percentage of people is\are coming to England this winter.
(1) Sentences like yours also confuse native speakers.
(2) I checked my books and wish to report this:
(a) The word percentage is indeed singular. But it appears that
many (most?) native speakers here in the United States follow
Of + singular noun = singular verb.
Of + plural noun = plural verb.
(b) Therefore, maybe many (most?) Americans would prefer:
A high percentage of people are coming to England this winter.
P. S. Should it be a "high" percentage or a "large" percentage?
I do not know. Hopefully, someone will tell us.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.