Do you know who installed the hidden existing cable between your master and slave sockets?
It might be possible for Openreach make a joint between the two cables at your existing master socket, but they might not be happy to use cable that they did not install themselves.
If you are not confident with following @licquorice's instructions, then as that work would solely be on the customer's wiring, you might find it cheaper to get someone locally to do it. Try a web search foe "Ex BT Engineer" etc - there are a lot of them about!
If @SteveG2460 has an unfiltered master socket, there is nothing to do. Simply unplug the router and plug it in in the lounge.
Why do I bother?
@licquorice wrote:
Why do I bother?
Some people just like to take the route that costs money because they think if you pay for it it must be the best route even if its not needed.
If you simply answered the question I posed, there is a possibility that you don't need to contact anybody and simply unplug the router from its existing position and plug it in the new, but feel free to continue ignoring my advice.
@licquorice wrote:
If you simply answered the question I posed, there is a possibility that you don't need to contact anybody and simply unplug the router from its existing position and plug it in the new, but feel free to continue ignoring my advice.
I was about to post similar but you beat me to it.
TBH, I had assumed that @SteveG2460 would try just unplugging their router and moving it to the other phone socket before calling someone out - if they hadn't tried that already. (As suggested by @licquorice ).
OP: if you haven't done that already, then try it - you have nothing to lose, it will either work, (in which case, problem solved), or it won't, and you will just need to put the router back as it was and contact someone if you don't feel confident moving the connections, (post #4 in this thread), yourself.