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[#1]

There is another socket in our downstairs cloakroom where the cable comes in from the outside. Then it feeds into the socket in the hallway which is the cable you see in the back of the master socket. It's probably been there ever since the house was built in the late 60's. We've had Openreach engineers out in the past and they''ve seen what we've got and not deemed fit to change it. I'm attaching photos of this other socket for your opinions. It looks a right mess.

[#2]

I have seen this kind situation several times and suspected it may be the reason for your problems.   This set up is (probably) the all cause of your issues. BT would not change anything in your home if it did not impact on the voice service , as it will be working fine for voice,  but for any broadband service  such dodgy wring  will be a severely  limiting factor for perfprmance .
Back in the 60's the preferred position for a phone was on a table in the hallway, so that's where the master socket and phone service termination would be situated, Back then it may not even have been a socket but simply a small junction box.   Extentions would be spurred off that point  to wherever they were needed, up to 4 maxiumum if I recall maximum REN ( Ring Equivalence Number) so you are currently working off a badly installed extention with plenty of opportunity for faults between the line entering the house and your "master socket"
The NTE5 style  materer socket you are currently using was probably not fitted by Openreach -  it appears to have a different makers stamp on it. or it may possibly have been swapped with  one in the hall . Anyway it,  and all that wiring could do with replacing . It does not look like a BT job to me!
Your best  option is to have proper master socket fitted by Openreach at the point where you need it in the house , and dispense with all the crummy extention wiring .
Unfortunately I very much doubt this can be classed as a fault with the equipment owned and maintained by BT Openreach: so you will have to pay up for proper the wiring and  proper NTE 5 socket  to replace what is there and to be insatlled exactly whre you need it. This is at the very limit of any DIY skills as it  would involve disconencting the phone line so should be carried out by a BT / OR engineer - If that is what you wish to do.
I'd budget for anything from £80 to £100 for the work but don't hold me to that. Could be more. Sorry there really is no cheap work around and BT /OR are not to blame ! 
Unless anyone has any other ideas?
Oh and using an electrician to make changes is not a good idea either unless they are fully conversant with phone & broadband connections which few are.
Best of luck!

[#3]

Thanks for the reply. I have decided to monitor the situation by disconnecting the phones for a period of time to see if that improves things and plugging them in one by one. Before I turn my house upside-down I may also have another try with my old router again. I suppose it's also worth disconnecting some of my wireless devices from the router.
Is there any possibility that it could be a setting in the router? When I got the new one last week, its username wasn't mine but the default tr09 thing. I set it up with my username and password but I'm wondering if I may possibly have missed something in the settings. The router is the 2704N. I had to put my Sky wireless connector on a static IP at the Sky box end otherwise my Android app wouldn't see it and the sky box would often be disconnected the next day. On the old router there was a range of IPs outside the dynamic pool which could be used for static IPs.On the 2704N, I found that when I changed the dynamic pool range, it wouldn't allow me to select an IP outside of the range to use as a static one.

[#4]

Hello

Quote

I have decided to monitor the situation by disconnecting the phones for a period of time to see if that improves things and plugging them in one by one.

yes  thats a reasonble approach . I woudld discinenct all the lose wire extentions from the  doubler sockets too! They could well be indcing problems to the line.

Tr69 is an automatic service which sets up your router with your Plus Net  use rname and password , which it detects from the Plus Net customer database and then reboots your router with the corect details . ( this is all detailed inthe nhandbook PN use dto send out with a new router) . IN theory all you need do with a new TR69 enabled router is plug in the router and leave it for roughly 5 minutes to do its business. A factory freash TR69 router is identified by the serial number which it sends back to the TR69 server at Plus Net  This serial number is assigned to you alone . The TR69 server sends your user name and password to the router which then updates itself with said user name and password and you are autimaticallyed logged in to PLus Net's network However , it does not always work and you sometimes need to manually do this yourself - as you have done .  if  you still saw TR69 as the user name then this is usually - in my experence - another symptom of a physical line problem and a bad connection .
There have been a lot of negativecomments about the 2704N router ;  I had one sent when I upgarded to fibre and for Wireless it was completely useless. Its in the cupboard and will stay there
The best option is a combined VDSL , modem/ router > The Billion Models are good.

[#5]

I just thought I'd follow up with how I'm doing. After screwing everything back up, I left the setup as it was and have been monitoring things. It seems much better now but I cannot explain why, other than disturbing the wiring may have helped.