Thanks. Here is what I have figured out thus far.
Openreach is associated with BT - part of BT's broadband networking efforts. Easy to find explanatory links etc..
Did you exchange fibre service for DSL? Or stay with fibre when you changed to First Utilities? Fibre is what I believe per the imgur image.
Your current setup is either FTTP (Fibre to the Premises) or FTTC (Fibre to the Cabinet). Green ended cable is going into the optical port on the Openreach router so my belief is that you have FTTC. I.e, an Openreach fibre modem.
The BT Hub 5 is set up on top of the white cabinet.
Which engineer installed the BT Hub 5 modem? Hopefully First Utility. Check your bill or service contract.
Note: if BT installed they may be expecting you to return the BT Hub 5 or will bill you accordingly at some time in the future. (ISPs can make money on obsolete devices left behind and not returned for any number of reasons.)
The leftmost box is the Openreach modem/router itself. The rightmost box is the battery backup.
Reference:
https://www.google.com/search?q=Openreach+fibre+modem/router&biw=1920&bih=963&source=lnms&tbm=isch&sa=X&ved=0ahUKEwi_sJab1ZLSAhVJ4WMKHYyLD7oQ_AUIBygC#imgdii=OoVe0o_if1qV7M:&imgrc=0cSDd5toTcSFHM:
Found a number of images and diagrams online: reflecting various models and configurations - fairly consistent overall.
So the present connectivity, as I understand it, is as follows:
ISP ---fibre --->[Optical Port]Openreach modem/router [LAN] ----ethernet cable------>[Red WAN]BT Hub 5 ====> wired and wireless connections.
So you need the Openreach modem/router to "accept" the incoming fibre. On its' own the Openreach modem/router provides wired LAN connections.
Then you need the BT Hub 5 to provide additional wired LAN connections and wireless connectivity.
To confirm, take a closer look and draw out a simple diagram. Use a mirror if necessary to look underneath the Openreach modem/router to verify the connections. The green LED lights and labeling should match the ports in use.
Not sure sure about the telephone connection(s). If your telephone service is via your ISP (being provided by optic fibre) then I would expect that the white cable you designated as "outside telephone line (white RJ11) really should be going to your telephone patch panel or maybe a central base station phone if you use wireless phones internal to your home.
If your home network and internet connections are all working as expected then the whole of it all is probably correctly configured. Key being that just one device (either the Openreach box or the BT Hub 5) is responsible for assigning IP addresses. BT Hub 5 is most likely right now with the Openreach box being just a "passthrough" and its network functions disabled.
The existing configuration all becomes moot if the BT Hub 5 needs to be returned.
So if the key question at hand is "can you simply replace the BT Hub 5 with the TG588v2 modem router". Probably not.
The cable from the Openreach modem/router [WAN (red)] would be expected to connect to a WAN port on the TG588v2 router. The connection will not be physically possible because the TG588v2 is a DSL device.
You may be able to configure some LAN to LAN workaround via the User Guides/Manuals for both boxes by model.
Three objectives:
1) Find out if First Utility service is fibre or DSL
2) Determine the BT Hub 5 ownership status
3) Verify and correct my line diagram.
Post script: Did someone really cut out a hole in the top of the cabinet so the power plug would fit? Overall appears to be a rather unprofessional installation. Kinks, twists, tangles, etc. will lead to problems and make troubleshooting difficult. Some clean up will be needed.