Also, if she is getting Council Tax Benefit the amount of the benefit will probably go down because you will be a "non-dependent" living in the house. The amount of the reduction depends on your earnings - which you would have to give evidence of to the Council.
If she gets Housing Benefit to help with the rent, the same will apply to that.
The idea behind this is that you - as an income earner living in the house - should make a contribution to these costs. If you paid your mother the amount her benefits were reduced by, she would not be worse off.
Her Incapacity Benefit would not be affected - it is not means tested.