TP-Link 600 Mbps 2-Port Powerline Adapter, Range Extender, Broadband/Wi-Fi Extender, Wi-Fi Booster/Hotspot, No Configuration Required, Wi-Fi Clone, UK Plug (TL-WPA4220KIT V1.20) - Pack of 2
Any good?
It's almost a certain that the out building will be on a different ring circuit to the house so won't work with any kind of speed.
You say running a cable is impossible, is there no fence or wall a cable could be tacked to?
Special cable for outside?
Special cable for outside?
Special cable for outside?
Proper way: cable and access point.
I wouldn't bother with a wireless link but the above suggestions might be fine.