You need to check whether you name is on the Land Register land title. If it is, part of the asset is yours, the other part is your mum's.
In England only, there are pretty clear rules about this now, since the absolute obligation was removed from local authorities. Your mum's capital, assets and savings are used to make an assessment, which is carried out by the local authority.
If the assets include a house, that house is disregarded as an asset if the spouse of the person going into care continues to live in it. The local authority also has the power to disregard the property in other circumstances - these 'other circumstances' seem to be at the discretion of the local authority.
The local authority also has the power not to order the sale of the asset to fund the care home and can instead agree a 'derferred payment order'. This is esentially an interest-free loan which is paid back eventually on the sale of the property. Local authorities generally ensure this happens later down the line by placing a Charging Order on the property, via the LR land title.
Local Authorities are wise to those about to go into care, their families and others attempting to avoid the obligation to pay. Firstly you need to find out whose name is actually on the land title. If your mum's name is on it, she shares the asset and it will have to be included in the assessment. Secondly, you will have to work with them to establish whether the 'other circumstances' might apply in your case. Thirdly, if not, you will have to see if they decide to invoke the deferred payment method.
Sorry if you live in Scotland where none of this applies. I haven't a clue what happens in Wales.