How difficult is it to travel around Moscow, knowing only English?

Not very difficult.
It is easy to get from the airport to a hotel and to major tourist sites. Some taxi drivers speak English and if they don't, they will at least know those popular locations.
Taking the metro around is also a good option, but not as easy. There are very few maps of the metro system in the stations and all station names and announcements are in Russian. But if you have a metro map, check the color/number of the lines and count the number of stations you should be able to get around pretty well.
In hotels and cafes or restaurants you should also be able to find people who speak English and the popular restaurants have English menus, so overall I don't see any issues if you stay in central Moscow.