Forget you have got a patch panel, simply think of your network as just long Ethernet leads. How would you connect things with just leads, it will be exactly the same using the patch panel.
The patch panel is only of use where you have multiple Ethernet ports to service it, i.e a router or a switch.
The simple answer to your original question is no.
From the ONT you need a connection to your router, but from your router you need connections to the rooms. You can patch from the router to the RJ45 in you cupboard to each room and provide ethernet to each room in that way. You will use one cable from router to ONT and 3 cables from router to the RJ45 ports in your cupboard.
If you want to move your router to the lounge you would have to patch the ONT to the RJ45 for the lounge and in the lounge patch from the RJ45 port to the router. There would be no way to connect the other 2 RJ45 ports in the cupboard easily to the router. There are ways round this but none are that simple. You could plug a powerline adapter in a mains socket in the lounge and patch from router to the powerline adapter, the plug another into a socket in the cupboard and patch from there into the RJ45 for the office and a second patch to the study (some powerline adapters accept 2 ethernet connections). Note that powerline adapters are very unlikely to give the performance as a proper Ethernet connection.
Why do you want to move the router to the lounge?
Sorry, forgot an important point in my last...
You would also need a 5 port gigabit unmanaged switch to connect the three patch panel ports together. Should be less than £20.
Thanks everyone for you help. I managed to move the router to the lounge through a combination of connecting the wan to the port in the lounge but this has just made there other 2 RJ45 ports in the house unusable. I dont really want to go down the route of using powerline adapters so it looks like it is a non starter
I some ways I am pleased with the outcome because it is what I had thought, its just nice to have confirmation from users who know more than me!
I only wanted to move the router for better wifi coverage in the rest of the house/garden but looks like I might go down the AP route to achieve that
Thanks
Apologies for causing confusion. Note to self to not hastily skim read & post before leaving the house!
The AP would almost certainly be the best solution.
So just run a single cable from the ONT to the wan port of the router. Then everything else on the network from the other lan ports of the router including any switches.
ONT to lounge RJ45 port. Plug hub in
Connect powerline adaptor to hub using one of the RJ45 sockets. In the lounge
Plug the other powerline adaptor into mains socket in cupboard.
Obtain a 5 port switch, plug 1 port into the powerline adaptor in cupboard, then each of your other ports on the patch panel plug into the switch.
Thanks, I tried that last night but noticed significant performance drop off from the other 2 RJ45 ports around the house. I have also tried a powerline adapter in the back bedroom and that seems to provide adequate speed into the garden.
I guess another option could be to change the Smart Hub router for something with better Wi-Fi coverage?