That sucks so bad because I called so many times to tell them the situation and they assured me we were only getting the amount of money a single person would get. Then they sent us all this extra money into our account and a letter stating that the money is based on two people. I have no proof that we ticked the right box on the application and they're not even getting back to me about making the corrections. I don't know what to do.
You have done nothing wrong. What tends to happen with benefits is, the first thing is to get the money out to those in need (although they are snowed under now) and they tend to sort errors or fraud later, as they can always get the money back from future claims, even if that means taking the money out of the persons state pension! Repayments to the government are not time barred.
You may not have a copy of the form you ticked, but you were quick to point out the money was too much as you were not entitled to it. Keep a note of every call you make, with the date, time and person you spoke too, but best of all....put it all in writing. Send letters from the post office as signed for (go on the royal mail site and keep a copy of the signature details) or take a letter in to the offices and get someone to sign a receipt for it. Or, if it is an overpayment of LHA, you can go to your council offices and talk to someone about it. Phone your council for their opening times for LHA problems, it is usually a ticket and queue system.
Just keep reminding them in writing and save the money so that you can pay it straight back when you receive the demand, to show you didn't take public money. The reason they might not have got back to you yet is because of the sheer volume of claims thay are getting now. Just keep all your evidence.
From reading other immigration forums, those who are getting refused ILR for claiming benefits are those that have not told the council/DWP/tax office that they have claimed in error.