I want to re-route my cable through a hole which means I need to remove a plug then re-attach. I have two options neither of which seem to unscrew; do I need to cut them off?

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Yes – cut them off

Just buy a screw on 'F' connector from B&Q to replace it

Fitting instructions here
http://www.satcure.co.uk/tech/fconn.htm

you can leave out the silicone grease for inside use

Oh OK thanks – was thinking I could reuse one of these plugs.

No – they're not re-usable

Just make the hole bigger 😉

It's an external wall…BTW, my reason for doing this is that I want to move the TV to the other end of the room but there's a fireplace in the way so want to route the cable outside using two holes that conveniently already exist – that's OK right?

that's OK right?

Perfectly – you'll need 7mm cable clips

just a thought, when my missus unplugged all our virgin stuff she fitted two plugs back into the router (i think) and got them the wrong way round, but they fitted…blew the router up.

or so the virgin guy said…..

The router only has one coax plug unless you mean the ethernet cables?

The router only has one coax plug unless you mean the ethernet cables?

One into the cable modem & another into the TV set-top box – the router normally just has UTP [network] cables going into it