I hate seeing posts like this as there is very little we (the community) can do except offer advice.
If you have an outstanding amount of £200 and money is owed to utility providers there is very little that VM (or any other provider) will be able to do. Services are paid for a month in advance. So you have been cut off to stop your debt increasing, not as a punishment for not paying.
The best advice I can give you is its time to reach out to other organisations, not the companies that money is owed to. Step Change are decent at what they do, Ive had friends receive help through them..
I would also be talking to DWP and see if they can support your family with an entitlement check to see if you are receiving the correct financial support for your situation. That can be done by an adult direct, or if you are in the position there is not an adult in the household who currently would be able to handle teh ins and outs of the situation, Barnarods have a help service for young carers.
Your immediate priority should be the utilities. As for internet for studies, most libraries offer free internet access, as do many government buildings. At a push, for the price of a coffee you can study in MaccyD's to your hearts content. I really don't want to patronise you, I sympathise with your position but it looks like you may have to do some out of the box thinking for next while , until things settle down with your families finances..