If the Openrech modem is showing that its connected, and the home hub is plugged into LAN1, then its either a home hub fault, or a fibre cabinet fault.
Did you check the BT Service Status page?
Yes it says it's fine
Then you will just have to wait. At least you have things connected up correctly.
It could still be a noisy phone line, so get a cheap (Less than £5) wired phone, and plug it into the bottom socket to see if you get dial tone.
If the phone line is noisy or has a high resistance connection, then that will affect your broadband.
The lack of any current flowing through the wires due to the lack of a phone providing an occasional loop, causes oxidisation at any joints which causes the line resistance to increase. This does not show up on a normal line test.
With Private Circuits it is common practice to allow a small "DC Wetting" current to flow through the line to prevent this problem.
There are quite a few people like yourself that do not plug a house phone in to check dial tone every so often. This can cause issues with broadband. Also, if one wire has become disconnected (quite common), then that will cause no broadband, constant disconnections, or a very low speed.
The solution is to get hold of a cheap (less than £5) wired phone, and plug it into the phone socket to see if you get dial tone.
Then dial 17070 (free call) and select option 2, quiet line test, and see if there is any noise on the line.
If you do not get dial tone, or there is noise on the line, then you need to report it as either no dial tone, or a noisy line. Do not mention the broadband.
Once the phone fault is fixed, then the broadband will get better. It will get fixed quicker, as there are plenty of Field Technicians who can fix phone faults, but not many broadband ones.
You may find that the very act of plugging a phone in, and getting dial tone, fixes your broadband, as it breaks down any corrosion.
An interesting thread here http://www.broadbandbanter.com/showthread.php?t=29287
Is it stuck in there? It should be released by squeezing the retaining clip in, then simply removing the plug.