Greetings
I'm sure it's possible, though you might have more luck through friends as people can be hesitant about allowing total strangers into their house.
You'll probably need to adjust your schedule to times when Brits are likely to be on holiday - those tend to be July, mid October and around Easter. I'd also make sure to have back-up plans in case the house owners' plans' change - with airline & train strikes you never know.
I'm pretty sure there are websites for this kind of thing, though I think many tend to focus on house-swaps - i.e. you'd have to let the people stay in your house in exchange for staying in their house. Otherwise house-sitting isn't always that much of a benefit - given the prices of electricity & fuel, it's often better just to have someone pop in once or twice a week to check mail & plants, rather than have someone living in and using oil/gas/electricity etc.
Kate