Marketing without business gcses/alevel

Am I delusional? To think that I can go into a Marketing and management course in university without studying business.

No you're not delusional. You can do a degree in marketing and management without studying business. A better question is why you want to do such a degree.
Unless you specifically want to study the subject for the love of it, want to become a business studies teacher, or you want to go into academic research in the field, then I don't really see the point in doing the degree.
For roles in marketing and the business sector, you can pretty much go in with no qualifications, just left school, or degrees in any subject. You would be expected to work and learn from the ground up.
If anything, if you want a specialised qualification, I recommend a professional qualification in marketing (the ones for management are by CMI, which I am not entirely a fan of) by CIM (preferred since they are internationally recognised), DMI, or IDM. Professional qualifications tend to have more up to date information, include more practical knowledge, cheaper, shorter, more widely accepted, and tend not to have any requirements for any prior qualifications.
Typical business degrees tend to teach you everything from the ground up, so even if you didn't do GCSE or A Level Business, you will be on the same page as everyone who did. In most parts, a management degree is essentially a rehash of A Level Business Studies.