I'm trying to decide between the online MBA degree at the Manchester Metropolitan University versus the Queen Mary University of London.

Obvious MMU has a triple accreditation, which is a plus point.

But the university ranks well below UoL in Times Rankings, despite the online MBA at QMUOL not having any of the three accreditations.

Which course should I choose and why?

I'd really appreciate someone helping me with my decision

The MBA at QMUL is newer and because of that it's not surprising that it lacks business accreditation. That will come in time.

I wouldn't use the general university rankings to compare MBAs. Instead look at the business-specific or preferably MBA-specific rankings.

What are your goals? 

You are mistaken. QMUL does not award an online MBA. AACSB accredition for QMUL is, as you say, just a matter of time. However, the online degree you refer to is awarded by the University of London. QMUL provides academic direction, but not the degree. UoL stands no chance of getting AACSB accredition. 

UoL stands no chance of getting AACSB accredition. 

The UoL has few of the requirements of an accredited university, most obviously it relies on other schools for academic direction and assessment,