Upvote:1
The rules permit you to do what you want. There's more detail in this answer
However, bear in mind that flights are limited at present, Schengen area borders are closed to US travellers, and non-essential travel is severely restricted in Britain.
This might change before you intend to travel, but at least one EU country is talking about maintaining the border closure until September (Source).
You would do well to keep your travel plans flexible, and perhaps take your holiday after your course.