Do go into the AGE UK website - all will be explained!
In a nutshell, SSD will step in and pay part of the fees when savings reduce to a specified level (which changes now and again). They will expect your Mum to contribute her pensions, and she will be left with a weekly amount of "pocket money."
The only problem that you might encounter is that the homes you are looking at are very expensive and sometimes SSD say that they will only pay up to a certain level.
So it might be worth speaking to SSD at this stage to find out where you will stand when the money reduces to the specified amount. If you can find a home that you are happy with that charges that amount it will save the scenario of needing to uproot your Mum from somewhere she is settled. Having said that a good SSD will try and keep someone where they are happy if they possibly can.
The other route that you might need to consider much further down the line is funding by the health authority - called continuing care funding - but the rules for this are very stringent and it does not sound as though your Mum is remotely at the stage where she might qualify. Please be clear that, if she does deteriorate and falls within those rules, she IS entitled to this funding in a care home - she does not have to be in her own home. In my experience, people's training in this area is sadly lacking and misinformation is rife.
I wish you lots of good luck in finding the right place. We "kissed a lot of frogs" whilst on this same search, but eventually found somewhere caring and kind, where both my parents (at separate times) live their last years and died in a warm loving environment.