Personally, I'd just focus on getting the right parking for you without worrying about a charge. As I'm sure you know, there is no such thing as modest cost parking, especially in west London..
Depending on the way you are planning to go, I'd also suggest the supercharging route. I have an LR, but I think an SR+ will still be more than fine with getting to south Ken via Oxford A40/M40. On the way back, you can stop at the Park Royal supercharger and top up quickly at the 250kw stands and be on your way home. You'll also go by it on the way down if you are desperate, but its a pain to get to as you have to pass the location, sit at a long light to cross the central reservation, charge, and then drive away from London to turn around at a roundabout again..