You could try a wireless extender in a window that does face the right way. Probably not much good for the cottage, but might be OK for "outside".
I hesitate to actually recommend this, as I have had really mixed experiences with different makes over the years. Some worked nicely for a few weeks then died for no apparent reason.
My current beast: "Netgear WN3000RP Universal WiFi Range Extender" has worked rather well for the last six weeks. It cost about £70 from amazon.