Weak connection on garage, first and second floors

The John Lewis link shows that the TP-link Deco X50 is out of stock. A quick google shows they are available elsewhere for a lot less, for example the 3 pack is only £179 on Amazon (£38 less than Argos, John Lewis and Curry's).

It's always advisable to purchase your own equipment although the VM pods would be free to you with having the Gig 1 Fibre connection.

I'll leave others to advise on the various extenders and the best way to connect/install them

Mesh systems are far better Ethernet cabled back to the hub when they effectively become just wireless access points.  Don’t forget with mesh systems each unit requires a power supply and are ideally placed not adjacent to the target equipment unless Ethernet cabled. I will not recommend any equipment I have not used. My preference is for ceiling mounted Wireless Access Points that use PoE (Power over Ethernet) for their power supply. I use various Ubiquiti WAPs including WiFi 7 ones.

If you are in the fortunate position of having a builder put in wiring, don't miss the opportunity!  Get Cat 6 ethernet cables pot into each floor, where you can install access points. This will be far more efficient than relying on wireless connections to each of them.  I would really consider getting ethernet to the garage if you can, because this is usually the worst place for WiFi coverage.

Agree with "flood" wiring Cat 6 cables to every floor,  with at least one socket in every room.  All to be terminated back to a switch.  This switch is then connected to the Hub, job done.  No messing around with Wifi backhaul to Mesh units, as they now can be connected with cable.  PoE would be preferable, as no additional power outlet is required, and these can be wall or ceiling mounted.  A compentent electrician should know what all this "stuff" is and can advised.  Come back here if you need more answers.

As for the garage, I strongly recommend getting the builder to run a cable here as well.  It can be up to 100Mtrs long, so distance shouldn't be a problem.

I have a Virgin Media Hub 5 that I would like to use as a modem and connect it to my own gateway. The cable from Virgin Media comes in through the front facade on the ground floor into the living room, where there is a white box from Virgin Media, which I connect to the router via a coaxial cable. Is it better to leave the modem (Hub 5) next to this entry point in the living room and then run a cat 6 ethernet cable to the gateway on the second floor, or extend the coaxial cable and bring the modem to the second floor, next to the gateway?

My latest reconfiguration of my downstairs setup, there are other switches around the house and also a NAS in the loft as well as an ONT for my second ISP connection. Those are the next to be reconfigured. All patch cables are colour coded to their function.

If you are going to have a mesh system, which is often a good thing to do, it's rarely right to move a hub upstairs - how are you going to get Wi-Fi on the ground floor? The best solution is most cases is to put the hub into modem mode connected to, say, a Deco system with the main Deco on the ground floor in router mode and with mesh nodes upstairs (and also in the garage in your case). You'll probably need a Gigabit network switch as well behind the main Deco, and you backhaul the mesh nodes with Ethernet cables to the switch. You also connect all other wired devices, eg PC, NAS, TV box, etc, to this switch. Do not lose the opportunity to flood wire your property as you have builders on site and do leave a draw string in each conduit.

"and you backhaul the mesh nodes with Ethernet cables to the switch." I agree, but then you are not using a mesh system as a mesh, just wired WAPs (Wireless Access Points). You do not need the ‘overhead’ of a true mesh system if you use it as WAPs, far better to just use PoE WAP units. No need then for all the mains requirements of a mesh system and the trailing wires. I have no visible wires in any of my rooms. The mesh systems I have encountered did not have many user parameters that you could tailor and a very small number of SSIDs. The WAPs I use can have up to 8 SSIDs per radio, that 24 in total. I have I many SSIDs set up with names like name6, name5, name2, name_5IoT, name_2IoT, etc. It also means you can put different SSIDs on different VLANs.

Your understanding of mesh is wrong. Mesh provides the following:

• Advertises one SSID (same network name)
  Coordinates roaming (802.11k/v/r where supported)
  Performs band steering (2.4 GHz ↔ 5 GHz ↔ 6 GHz)
  Shares client state and topology
  Acts as one logical system, not independent APs

By using wired backhaul Mesh is more efficient than wireless backhaul which causes a degraded system due to the inevitable inefficiencies which we are all too aware of with wireless system.

Furthermore I do not recommend a WAP as most people just want a plug and play system like a mesh. You may like playing around with tuning a WAP or spending money on a controller like UniFi, but this is not applicable for most residential users.