If it's the Home Hub that's faulty, and if you are out of contract, then the Hub is yours and it's out of warranty. If that's the case, then it's your equipment that's broken and it's your problem to fix it - just as if it were your computer that was broken.
If it isn't the Home Hub, then that's another matter. BT are responsible for maintaining the broadband connection.
There's a site on the internet that begins with "e" and ends in "bay" where you can pick up quite cheap Home Hubs. That's what I did when my last one went flaky.
Alternatively, phone Customer Options (the number's in an earlier post), and practice your haggling skills. You should be able to get a new Home Hub and a discount on what you're currently paying. I haven't paid full price for years. However, there will be a new 12 month contract.
The Ombudsman will do nothing until you have been through the BT complaints procedure and given them the opportunity to resolve the problem. If the problem has not been resolved you then have to ask for a deadlock letter which should explain what BT have done to try and resolve the issue and why it has not been resolved.