OK, an update on this... I've not been well and also a bit wary of disconnecting and reconnecting the line too often, so spaced tests a few days apart.
Using a new EE SuperHub I get the following results:
With 5m cable:

46.92 Mbps / 8.19 Mbps
with 5m CAT5e cable:

56.41 Mbps / 8.16 Mbps
using 3m cable that came with router :

60.76 Mbps / 8.28 Mbps
The download speed has improved since using the new Superhub instead of the old Brightbox2 although upload speed has dropped. That is, when using the supplied cable as that gives best download results.
The Brightbox 2 gave me (using the supplied 2m cable)

58.49 Mbps / 9.77 Mbps.
The best I ever got from the Brightbox2 was

60.21 Mbps / 10.86 Mbps
I'm lost when it comes to finding info about power output but I'm not daisy chaining cables, I'm swapping out the supplied RJ11-RJ11 as it's too short to put the hub on a safe shelf. Instead it's sat at the far end of my desk with the wire over the fireplace between it and the Openreach socket.
I'm also confused by the suggestion to use a RJ45 to RJ11 cable? The RJ45 is the phone outlet isn't it? That would need a filter, which then goes to a RJ11 socket. I have such a bit of wire but it does nothing when connected to the hub. I didn't think it would.
CW1308 is mentioned, that is telephone cable - I am talking about the router connection, connected to the RJ11 (filtered) socket of the Openreach 5e.I don't have any extensions. The Openreach socket was a new install in July 2017, I hadn't had a 'BT' line in about 20 years so the line had to be re-provisioned. Lots of tests done at the time, some of the external wire replaced, all OK. The only change was to swap the front plate to the dual outlet, rather than have a splitter dangling.
Again, looking at the four different cables I've tried, I would discount them all being dodgy. One is, as noted, made with CAT5e cable and gives the inbetrween result, but still lowers the download speed.
I think I have previously said that the cables are run over the same route, I don't move the router to a different position, even though that's what I want to do. I don't leave them coiled, I unroll them and do my best to have a straight run without bends. But, for the hell of testing, I tried running the new 5m cable where I wanted it to go, under the carpet edge around the fireplace and up to the shelf where I want the hub to go I lifted the hub up, connected it, and got the same results...
It's got to the point where I don't think I'm going to get this to work. A suggestion to try a longer length has not yet been tried. I will order one and see what happens, but am giving up on this one. Te hub will have to stay where it is. It's got it's own patch in the dust on the end of the desk now...
For those that want to know. Here are the cables I bought:
5m -
https://www.ebay.co.uk/itm/5m-RJ11-ASDL-Cable-Black-...
5m CAT5e -
https://www.ebay.co.uk/itm/5M-Metre-RJ11-to-RJ11-Hig...
I had bought another 5m RJ11-RJ11 but it's gone off my purchased items list now.
I also used the supplied cabled from the brightbox2 (2m) and the superhub (3m)
All were run the same distance between the hub and the socket. I also tried taking the faceplate off an using a splitter in the test socket, no difference noted.
EE Fibre Plus