I assume this means that if the course is 90 days or less, no visa is needed. If the course is over 90 days, then a visa is needed. I don't imagine you can't use the visa exemption for up to 90 days then get a proper visa. So it depends on the length of course the OP is doing. If you arrive in Spain with documents for a 3 year undergrad or similar, the border guard is going to want to see a proper visa.

Of course, you can enter as a tourist, get set up, then fly to London, and come back. Not 100% how you're meant to do it, but feasible. Also worth noting, in most countries it's illegal to have two valid passports of the same nationality on your at the same time (when abroad). If the OP gets searched leaving Spain/entering the UK with 2 valid US passports, it might not be a great outcome. I have two passports, and was told when the second was issued that I could only use one at a time, and the other must remain in the home country.