Assuming the garden office is on the same electrical circuit as the rest of the house, you could try a
homeplug wireless extender. One end gets connected to the router and plugs into the mains. The other end plugs into the main in the office, and provides a wireless signal there. I'm not sure what actual speeds you will get, but the ones I have do provide a solid signal.
Edit: what ^ he said, except the ones I linked to provide a wireless signal as well.