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Well done for the work you have done - although readers could also consider some other methods. Wake on Lan being mentioned already - If you don't want cables, my Dell Laptop will Wake on Lan over WiFi as long as its power adapter is connected so check out it yours will. For a desktop that I didn't want to run ethernet cables to, I used a ethernet over the mains adapter and this then gives Wake on Lan to the PC. You can also get a Belkin Mains switch which you can control via a DO button on your phone. Just set the BIOS to turn on when mains is applied. You mention that TeamViewer is free. Yes it is free for personal use but users should not that commercial use requires quite an expensive license.
I don't want to detract from the work you have done as it is a very good solution. I've also recently purchased an ESP8266 and will be using it soon. I use the Belkin WiFi switches for some of my similar requirements. You mentioned that they are expensive at £39.99. I paid £24.99 with free delivery from MyMemory.co.uk http://www.mymemory.co.uk/Belkin/Smart-Plugs and also bought some from Maplins at the same price as they offer a price match. My Ethernet over mains were a present so that was a no brainer !! Thanks for your instructable.
You can configure Teamviewer to be permanently installed and use a fixed password but remember Teamviewer is only free for personal use. There are other remote control apps which are free.