I agree it is about 10 min, but depending what day of the week it could be a bit hectic. The area around the hotel is mostly business, so M-F it gets crazy busy, especially during morning and evening rush hours.
The sidewalks have a mix of concrete and cobblestones, so it wouldn't necessarily be the best for a stroller.
Once in the Tube station, you'll need to find where the elevators are. I know they have them, but I've never used them. The track is rather deep down from street level, and I don't think you'd want to take the stroller on the escalators.