I realise this question is from 6 months ago, but anyone with an impairment that falls within the definition of disability by the Equality Act 2010, formerly the Disability Discrimination Act 1995 has to be provided with "reasonable adjustments.
What is now Virgin Media who took over the fibre optic service installed in the late 80s by Cable and Wireless offer all customers who meet the criteria a free back up mobile phone and sim card... the OP in this discussion will meet that criteria.
The law states that a person cannot be put at a disadvantage due to their disability by any service provders... that applies to every organisation from high street retailers to police and even the NHS.
BT will not volunteer this legal requirement, but anyone reading this post can contact BT and demand they abide by the Equality Act 2010 - by the provision of a telephone device that can be used in the case of a power failure.
If you need help asserting your rights the Citizens Advice Bureau should be able to advocate on your behalf or the regulator is the Disability and Human Rights Commission as this roll out is going to put thousands of vulnerable adults at risk of harm if the power fails in their homes.
