I am not sure where you wanted to be in West London but these guys
Storage | Duke Of London have a good reputation amongst some of my friends who have classic cars. They are in the Kew area so new the M4/A4 routes and outside the ULEZ are I believe. They have events etc going on too plus maintenance capabilities although they are not Corvette specialists.
On trackers I like them for basic security reasons and can help with insurance costs. I would especially have one if my car is in storage since the newer version will alert you if you car moves without your approval and where is does move to. Also get one that tells you what its battery state is. Nothering worse than picking-up upo your car from starge to find the cleaner has unplugged your tirckle charger and also your tracker will fail if your battery goes flat.
If you go for an underground facility, make sure your tracker still works in there otherwise things like battery status probably won't work until it is above ground.