A "Wireless Access Point" is not the answer. Think of the WiFi adapter in a computer as the "sending" device and the Wireless Access Point (in a router) as the "receiving" device, thus they communicate.

Installing a second Wireless Access Point for the TV won't be able to communicate wirelessly with the router, as they're both "receivers".

What you actually need is a "Wireless Network Bridge". This is the opposite of a Wireless Access Point and lets a "wired" network (your TV connected by ethernet cable) connect to a "wireless" network (your wireless router).

Yes, you're right. Of course a WiFi adapter and a Wireless Access Point can transfer data in both directions, I was merely explaining in over-simplified terms that two Wireless Access Points cannot communicate directly. The same isn't true, however, for WiFi Adapters because they can be configured to operate in "Ad Hoc" mode and be networked without a Wireless Access Point ("Infrastructure" mode).

I hope what follows isn't patronising.

Mains networking simply sends the data signals over the mains wiring - live and neutral. Each plug incorporates circuits that protect your computers and other devices from mains voltages and currents, and codes the data at frequencies suitable for transmission over the mains. Treat it a bit like a normal ethernet with mains running on it!

I have 4, 200mbps devices. Three are on one ring main and the other is on the other ring main. So the signal to the one on its own ring main goes via the consumer unit to the furtheest part of the house. It just works. Try it!!