I assume you have checked for updated firmware?
That particular router is not great - have a look at this one:
I am not a fan of homeplugs and I have no idea why what the issue is with 2 pin plugs - they come with UK 3 pin?
You could run an Ethernet cable outside but will either need to use exterior grade Cat 6E cable or put in a conduit. A single Ethernet cable, whether indoor or outdoor, is only designed to function over a distance of about 100m (328 feet). Some networks operate successfully with Ethernet cables run 200m or more. When extended past the recommended limit of 100m, Ethernet reliability and performance may suffer, and results can vary from one cable to the next. Active hubs or other repeater devices can be installed with a series of CAT6E cables to greatly extend the range of an Ethernet outdoor network.
A repeater is cheap. Dont know much about them though - but if you buy a a new dual band router make sure you buy a dual band repeater like this one