Yes, we should be able to install a phone and internet in your garden office, but it sounds like it might take a bit more work than normal. We would either need to dig a small trench for a cable to be run outdoors, or run the cable along a fence or some structure, it would really depend on how things are setup at the location. Since it would be considered inside wiring work, there would be a charge for it. You can speak with our sales team to have that arranged.
Another (possibly simpler) alternative would be to get a wireless phone and router, but this would depend greatly on the distace your garden office would be from the main office.