Thank you for contacting the Intel Communities.
Regarding the Wake on LAN feature, some settings have to be present in your router and also your Intel® Compute Stick.
Intel® Compute Stick settings:
Go to Device Manager and right click, select properties for the wireless adaptor. Enable Wake on Magic Packet
The feature Wake on LAN has to be enabled in your router also, in order to get the instructions on how to perform this, my recommendation would be to contact the manufacturer of your router.
Thanks for the reply but, unfortunately I discovered that while I could enable the Wake function on my PC the basic modem supplied by Sky here in the UK does not provide the required facility ("this is not a function that would be required by a normal household" they say). Also, unfortunately, they do not allow the use of any other router but theirs on there fibre network.