I am sad to hear so many people being harsh on Rach R, cos she clearly has only just started to think about the financial aspects, and has initially seen them as unfair. Some of you are also very simplistic in your responses. Here is mine.
Rach R, your mum has some funds, more than many people have. She will therefore be expected to pay the full cost of any care home until her savings go down to £23,250. At today's rate of care home fees, that won't be long. After that, she will have to pay a proportion of the care fees until her savings drop to £14,250. If she owns her own home, this will be taken into consideration for future payments. You don't have to sell it. But mum would be charged full fees, and the shortfall (after deducting her pensions) would be taken as a charge against her home whenever it is sold. You could rent it out, and use the income to contribute to the home fees, less income tax on the rental profits. Or could do nothing and accept that when the house is sold, a chunk will go to the local authority to cover the growing debt. Not all authorities accept this system, so check with yours.
I can see where people are coming from who suggest that there isn't a problem, and that you are very lucky that your mum has savings. The problem I see is that if you choose a home you like, and can afford, when mum's savings are gone, and even when the house money has gone (which might not be a long time), your mum might not be able to stay where she is unless the Local Authority fully fund that place. She might, in fact, have to move to another care home where the fees are lower.
There are "top up" schemes in some LAs whereby if the home you choose is not fully funded by the LA you can pay the difference. Unfortunately you can end up paying the difference for a long time, and this money CANNOT come from your mum, it must come from a family member. It is a regular commitment that is difficult to get out of if your circumstances change.
So I don't envy your situation. I don't pretend that it is easy. Look for a home that suits your mum and ask what will happen when her private money runs out. i.e. Will the local authority pay for the same bed in the same room (my mum's authority would have paid for a different room - a dim and dingy room by comparison with the bright sunny room we were paying for).
But to answer your question, no, you cannot do anything to transfer monies from your mum to you. If she was in the habit of doing so over the past few years, then that could be acceptable. But any sudden transfer of monies would be seen as "deprivation of assets", to avoid paying care home fees, so don't even think about it.
Hope this helps.
Margaret