Back to update as promised. In the end we got the Amazon Fire TV stick. Was going to get the Fire TV box and cable up, but decided to see how it worked over wifi since the signal seems okay and if it's not we can always get a box and use the stick in the guest room (which is nearer the router).
It works great, and is a nice little device. Put Plex on it straight away and installed the Plex Media Service on the HTPC. Super easy and quick to set up and streams fine over wifi. I guess if we were trying to stream lossless 4k content or something we'd need another solution, but for what we're using at the moment it works a treat. Really pleased with it.
It even seems to wake the HTPC over the network, which is a nice feature.
The startup times are a little slow, both for the stick itself and the Plex app, but otherwise it's great, especially for the cost.
Although... the stick did just bug out and throw up "connected with problems" "not connect to the internet" problems, which only cleared up when I got it to forgot and reconnect to the router. Hope this isn't something that becomes a regular annoyance.