Also, how slow will it go? Will it stop working completely?
You are probably already on the slowest speed.
Which BT Home hub do you have?
You could be re-graded onto a fixed speed rate option which would solve the problem.
Fixed rate can normally be arranged, but see if its an option for your line.
In order to find out what services are available, please enter your phone number into this form.
Broadband availability checker
Please remember to edit out your phone number before you post the results.
There will be a line specifying fixed rate options, usually only up to 2Mb though.
Is it not possible to power the home hub directly from your batteries, there are quite a few efficient DC-DC switching inverters available?
I am going to ask one of the moderators to help you with this, as there may be other options available in your case. It will be easier than trying to explain it to the helpddesk
What voltage is your solar battery, because the current consumption will depend on that. Not sure what the HH4 DC input voltage is, but if its 12v at 1.2A, then at a higher voltage, with an efficient DC-DC converter, the current will be less. The wattage will be the same, plus a bit for converter loss.