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You won't have capital gains tax liabilities when your mother passes on. You inherit the house at the value as at the date of her death. CGT would only be relevant if you keep the house for any length of time and aren't living in it. CGT would possibly become due to the uplift in value. There may be inheritance tax to pay depending on the size of your mothers estate but that would be the case whether her estate was in the form of a house or if she had sold the house and put cash in the bank. Happy to discuss further but I don't see that downsizing would save tax of any description for her and as you say she would have the stress and expense of moving. I hope that helps. Please leave a positive rating so that I am credited for my time.
If you rented the property you would have the net rental income and an asset that is likely to appreciate in value more steadily and one would hope more safely than paper investments. You would have a CGT liability potentially on any increase in value from the date of your mother's death but you could set off against that capital improvements and you also have an annual allowance, double in fact if you have a spouse with whom you could share the title to the property.