I think the misunderstanding is the assumption about form factor. The 7050 series is available in a case the size of a paperback book.
Despite DELLs willingness to slap the same series number on everything from an ATX tower to a "paperback book", they are far from the same thing.
I'm willing to accept I may be wrong, so let's see.
First page, the one on the right. I don't see why you'd doubt an 8-watt idle, since it's basically a laptop processor and chipset. Please note that these models are available with both 35W and 65W TDP processors; I'm talking about the (generally cheaper) 35W models, of course.
I doubt the original poster is talking about the small "book" sides micro form factor at ~$40.
I expect that one to cost at least double, if not more (a quick eBay search outs the micro form factor at closer to a £200 average), and the tower form factor, with it's 240W PSU is likely to be drawing much more than ~8W in a typical configuration.
My point stands; if you want to spend £35 on an x86 machine, youll pay in electricity costs, spend ~£200+ and overall youll likely save money overall if it lasts a decent period.
if you want to be sure, use an old (skylake and above) laptop and give it a usb3-eth plug. my latitude e7470 idles at around 3W (powertop)