I think you will struggle to find anywhere which will accept you with a BTEC in Applied Science, would you be able to switch to Engineering?
I would also be aware that there is very, very little aerospace engineering industry in London, so if you intend to stay in London after graduation too you should consider that your job options will be very limited. The closest place with a significant aerospace presence which is somewhat commutable from London would be Oxford.
The options for becoming a pilot are very different to studying aerospace engineering, so I would look into that separately. It will almost always involve either a significant cost (in the hundreds of thousands of pounds from what I remember) or a commitment to the sponsoring company(/organisation in the case of the RAF) to work for them for several years after you complete your training. It's a bit more viable to go your own way if you go for helicopters instead, but still a very expensive route.