The red patch cable to the router is fine and should not be touched for the purpose of trying to find out why you cannot get ethernet to the garden room.
As @licquorice has said you still need 2 other patch cables one to go from the router to the ethernet socket in the house and one to go from the ethernet socket in the garden room to the laptop. We need to make sure both of these cables work correctly and the easiest way to do that is to try each connecting the laptop to the router. If the laptop can reach the Internet with each cable then we will know the problem is not them. So please try each of the two cables and see if they work between router and laptop and report back.
We have to take things one step at a time to try and isolate exactly where the problem lies.
So are you saying the cable from the shed doesn't terminate in a socket, but has a plug on the end of it that you have plugged into port1 on the hub?
The cable in port 1 looks like a home-made cable, (as opposed to shop bought). I know you said the sparky had put sockets in, so where does that cable connect to?
Edit: Ah, me and Licquorice are thinking along the same lines.
@licquorice @countrypaul I think this may be the issue, as you can see from the photo below, there is no socket on the wall from garden room cable into the wall so there is therefore no patch cable from that socket into the router. I take it this would solve it?
Yes, that explains a lot.
Can you take a photo of the garden room end ?
Socket top left and then I planned to feed it into the ports through to hard wire the TV, PS5 etc.
You can't just do that, you need an Ethernet switch to feed multiple sockets
I'm still not clear what is connected where.
Does the cable that is in port 1 of the hub go directly to the shed?
Yes, straight from the router in house, through the wall (no socket in place), down the garden and into the socket in the garden room.
So you have a short cable (patch cable) that you can plug directly into the hub and you laptop that allows the laptop on the internet.
In you plug the cable the electrician fitted into the hub and the patch cable into the socket the other end of the electrician fitted cable as well as the laptop the laptop fails to see the internet.
Is that correct?
I suspect it was the reference to sockets earlier that made some of us make incorrect assumptions.
And yes, I realise I need to by a ethernet switch between the socket in garden room and the ports. Just want to get the actual internet working first.