Hi Robert
You could use MPs for this situation, but you would need a fairly high level of technical expertise to set it up, and it is overkill.
The BT Hub5 router has a wifi Access Point built-in, so all you need is a device that can act as a wifi client and provide the Ethernet connection for the TV.
I have used the TP Link MR3020 devices for this purpose previously. They are compact devices, work well and are easy to set up.
You set the device to WISP mode (with the switch on the side), then set up the client side ID and Passphrase to match the wifi on the BT Hub5. It is also worthwhile to disable the internal Access Point in the MR3020 as you won't need it.
You can use a second MR3020 device in the shed if the wifi signal reaches there strongly enough. If not, you may have to use a different device with better external antennas to pick up the wifi signal.
Probably worth finding someone with some wifi experience to help you set it up if you have not played with this sort of stuff before.
Regards
Terry