does anyone know the best place to look for cheaper broadband?

@BrianMcFaddenfan24 Are you living with your Mum? If you are not living at the property, then you would not be able to get social broadband for your Mum's property.

Social broadband is only for people that are claiming benefits, you would have limited speed and maybe a block on how much you can use it, such as download restrictions.

In the old days, you could not go to another provider, as if you tried to switch from Virgin to BT as an example, Virgin would say that there is a hold on the line due to an outstanding debt.

If say for example in the past, when you had someone with bad and existing credit and you moved into that property, then the phone company would be weary and you would have to provide more proof of who you are, before the line was unblocked.

Your Mum would still be liable for any contract that she still has left, even if you switched providers and potentially that might involve bailiffs at a later date.

You have said that you have offered to pay for her, and was refused. You could do one of two things

1. You could pay the bill with your Mum's knowledge and form a repay system, so that she feels better about herself.
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Any move or transfer, especially if you want to keep the phone number in the old days would be impossible, I am not sure what it would be like now, but I would imagine that they might have the same system, even though I think I read that things had changed now, because they class having the internet the same as having water.

Hopefully, one way or another you get the bill sorted.