Okay..

Im currently in the UK, (filing for CR-1 through Vermont). We are hoping for a case complete by late September, Im just wondering how long people are generally waiting for an interview in London after their case is completed

I think this depends on the visa you are going for, I see from yours that you are CR1/IR1. I have seen these get interviews within 5-6 weeks from leaving the NVC but that can depend on how busy the embassy are I suppose.

We are currently waiting for our interview date now and we were case complete on the 9th August, we know that our papers have left the NVC so now it is a waiting game (again) We are hoping for an early October one.

It really depends. After your case leaves the NVC and arrives at the consulate it can take anywhere between 3 weeks to a few months, depending on the country. UK should be one of the quicker ones.
Late September might be wishful thinking, but October sounds very realistic