Either move your router nearer to the garden room or move the garden room nearer to the router!
It might be easier and is the best option, to run an outdoor Ethernet cable from the router to the garden room and use a wireless access point in the garden room to allow wifi connections. This assumes there is electrical power in the garden room.
If running Ethernet cable is not possible, and assuming the garden room has electrical power and is on the same consumer unit as the house you could try using wireless powerline adaptors You would plug the "master" into an electrical socked near to the router and connect the router to it by an Ethernet cable then plug the wireless powerline adaptor into an electrical socket in the garden room. This would give you a wifi signal in the garden room.
See link for powerline adaptors. You do not need to use BT ones.