This is tricky.
She can of course give you the house as a gift, but if she continues to live in it she could be said to be deliberately disposing of her assets in years to come. This is called a 'gift with reservation' as she is reserving her right to live in it.
And if the house was sold in the future, you and your brother could be liable for capital gains tax from the date of the gift.
The local authority now has huge power to claw back assets that have disposed of in the way you propose - you and your brother would be liable for any care costs, or a charge could be put on the property.
If you or your brother ever got in to financial difficulties, your mother could lose her home. Or if either of you got divorced, it would be an asset to be taken into consideration in the divorce settlement.
But would you really want to see your mum go into the local authority care home that has been allocated to her, rather than a private home of her choice, if that day ever comes?
There are all sorts of trusts that can be set up to avoid inheritance taxes, capital gains tax and care home fees so that other tax payers would have to pay for her care, but it is very complicated and you need expert advice.