Purely from a moral point of view you need your Mum to see either her own or an independent solicitor on her own. Morally, it is up to your Mother what SHE wants to do with her savings and NO ONE else unless she is incapable of rational thought. By you either asking or suggesting what she should do could put pressure on her and she may tell you what she thinks you want to hear for fear of upsetting you?
If you are serious about HER welfare try and get some facts, figures and info from your local council and maybe an assisted living provider like Abbeyfield homes. Give all of this information to her/a solicitor but then let her consider her legal options and wishes independant of any outside pressure.
Another thought for you would be to ring your local tax office to find out the exact tax implications for financial gifts. They have specific rates and formula for this type of dilemma and are usually very helpful.
Good luck