If your mum has a financial advisor, did she not check this out before she went ahead? It is the very definition of a contrived tenancy.
A tenancy agreement means nothing, everyone who wants to claim needs one. Paying the market rent is a small indicator that is usually used when the property was previously let to unrelated tenants. It shows that no loss was incurred.
Your mum would likely need to let the house out as a landlord, to an unrelated tenant, before you could realistically try and claim HB or LHA for it. Then paying market rent would be important because you could show that your mum incurred no losses letting to you and is treating you the same as a normal tenant. She'd need to prove that she is a landlord first, though.
As she bought the house to let it to you, the tenancy was contrived, and you will be turned down. Not declaring that she is your mother will end badly because they'll find out, and then you could be prosecuted and end up with a caution or conviction for fraud, as well as having to pay back every penny - and they will soon have the ability to recover over payments from other benefits, so you'd risk your CTC. I believe they can currently take 25% maximum, rising to 45% shortly. There is a question that asks if the house is owned by you or family, so you'd have to lie in writing and repeat that lie at every renewal.
If your mum can't afford for you to live there without HB contributing to the rent, which is perfectly normal and understandable, she'll need to let it on the general market and you'll need to find a property not owned by a family member. In a few years, you could ask the council to consider it as a normal, non contrived tenancy, but the rules on this are tightening and it'd probably fail, to be honest. It's so strict now. It didn't used to be, but new applications are checked strenuously.
I know it's not what you want to hear and I'm sorry (although I have nothing to do with making the rules!) but it's better to find out now than further down the road.