Is the concern just over not being able to pay the bills?
As promised on the phone
This should be relatively straightforward to deal with.
I am answering this as though I’m speaking to the surviving brother.
You have documentation from the coroner and presumably the crematorium and undertaker.
Copy those documents and treat them as the death certificate and send them with a covering letter to the creditors explaining that you are the brother of A who died on the date that he did in May.
He had an accident on such a date, he was in hospital on such a date and died suddenly on such a date. As a result of his early demise, there is an inquest and you are still waiting for the result from the coroner. Meanwhile, you do not have a death certificate because the cause of death has not been established.
Can they please therefore suspend collection of the accounts in your late brother’s name and open new accounts in your name from whatever the date is in May when your brother passed away you will need to come up with an estimate of what the meter readings were in May and you can probably do that by looking at previous bills.
Tell them that as soon as you have a death certificate you will be in a position to finalise your late brother’s estate and to gathering any assets settle any outstanding bills and he would appreciate if they could mark their file accordingly meanwhile and of course open new accounts in your name.
If they ignore the correspondence, right back again in exactly the same terms or better still, get a solicitor to write to them.
You should find that once they know the circumstances, they become more sympathetic. You just need to make sure there is some proof of the death which you have in the form of the existing correspondence.