BT Tech support will be able to deal with this ... but to be honest you will need a UK based office to deal with it and understand the sensitivities.
They can set up a new account with a new user name and have that running in parallel with the original. Then they can migrate the individual email addresses across to it before arranging for closing down of the existing account and they can - if so desired also move the email address of the deceased to become as subsidiary of the new account.
It might be that you call the UK based Business support desk - in the last evening when they are quiet and ask them for advice and if they can provide contact details for a suitable person/team to speak with on the residential side.
I had to investigate and partially implement something similar a little while back - although it was on BT Business.
M H C
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