On one wall, we have a traditional TV aerial point. Plugged into this, the TV works well.

But we want to move the TV to the opposite wall (15'?). Rather than running an untidy wire round the room, is there something we can plug into the aerial point which will throw the signal across the room?

(We know from experience that an indoor aerial doesn't cut the mustard.)

Most wireless extenders seem to be intended for sending the HDMI signal from one device to another, not for extending the raw TV signal from the aerial. I would imagine the frequency range such a device would need to handle would be very wide.

To be honest, all we do is use a powered/amplified indoor aerial by One 4 All, it saves having to have new cables run down from our original loft aerial. One 4 All have various designs and different levels of amplification to suit your signal strength.

Maybe you could run a freeview box plugged into the aerial socket, and wirelessly transmit the HDMI output of that box across to your TV using a HDMI wireless transmitter/receiver (you can find those on amazon).   If would mean having to point the remote where the tv was not where it is now 

I'm more in the corner of............
There's so much  being broadcast it's the TV itself likely to go across the room.
Nick's solution sounds good.

The simple answer is yes there are things you can get to do this, but, (there is always a but) they cost a lot of money, RF is a dark art with high frequencies and multiplexed and encoded data each channel is about 3-5mbs. If you don't like the look or arial cable running around a room, then the other options are RF to cat5 and run a cat5 around the room as you could take a longer route, IP encode the incoming however you'd need to decode each channel, and use and IP tv system.

Thanks, everyone. I wondered if there was some common gizmo I didn't know about. In this case, evidently not!