Parking in London, (Paddington)

Help!
I never contemplated to have a car in London, but as I need to get some things across the Channel, I have to go by car and find a place to leave it for a week. As I don't have a car permanently, I'm not entitled to a residential parking permit.

Anyone a tip where to park a car in Paddington without paying more for the parking than the car is worth?
Or would you leave it somewhere outside Central London to collect it later - again: any tips for safe and reasonably priced places?

There is a >50% chance of me not having the problem at all, because I'm unlikely to survive my 1st attempt to drive in London. But I want to be prepared for the unexpected and know where to park should I get through...

thanks!
Sven