AIBU to ask for advice ? Ex H has died - complications !

[SortYourselfOut]

This is all in the UK.
Had a knock at the door last night from one of these 'heir hunter' people to say that my exH has died, it happened about a month ago but they didn't have any info of next of kin etc. We have a DD, she's 24, hasn't seen or heard from her dad for about 5 years.
He has a house, no mortgage and so DD stands to inherit this.
He was a 'difficult' person, there was certainly no love lost there on my part, but we are still in shock and discovered today that it was probably an accident and that he suffered quite a bit at the end, he wasn't discovered for some time. I've kept this from my DD, she is upset as it is and she also has special needs. I'm so sad to learn this, poor b*gger didn't deserve that.
Practical matters - he hasn't had a funeral yet, he's having one supplied by the council (what they used to call a 'pauper's funeral) and I shall make it as nice as possible for him. None of his family relatives know what has happened, he was estranged from them. I'm waiting until I have the funeral details before I try and contact them.
He lived alone, he worked for a large company I've tried to get some info from them today but they can't find anything yet. I want to see if any of his colleagues would like to attend his funeral or send flowers.
I suppose I'm just asking on here for advice as to what I do next. I'm prepared to empty his property and put it up for sale for my DD but where do I start ?
I'm also a bit nervous about seeing his friends and family at the funeral, he has really spread a lot of untruths about me to them, saying I kept our DD away from him but it's not true, she wanted to stop seeing him years ago, in fact we moved from living a 4 hour drive away to closer to where he lived so that they could have contact (one of the reasons) but he was so tough and unreasonable to deal with that she stated simply she never wanted to see him again, his family and friends only know his side and he blames me. So I'm a bit anxious about that although this isn't about me, I still want to give him a good send off.
I need a solicitor, don't I ?

You need the death certificate. Speak to the coroner. I don’t think you do need a solicitor.

(Edited incorrect info, sorry) The death certificate is required to show to banks to access his accounts. I doubt an estate agent will request it (until you tell them the circs) given all the horror stories I’ve read about people attempting to sell houses they don’t actually own.

Cross posted because I took so long to write everything so edited given your latest posts.

The Council will have engaged them to get their money back for the funeral. Presumably they know he owned a property.

I don't think you can authorise the heir hunters to do anything for you, given you're not the one to inherit, and particularly given your daughter has special needs.

@SortYourselfOut well if you are certain there are no other children, once you get permission to enter, change the locks first of all!!

Who has his belongings/keys-are they still at the hospital?

But you can't just do that - he might have written a will leaving everything to someone else.

I am glad to hear that you are getting legal advice

There is no reason why you cant take over organising the funeral.

The Council only does it when no one else comes forward to do it. There was one case I came across where a former employer arranged a funeral and another where a village organised a funeral for a baby found dead in their area.

I would also look at putting the money into a discretionary trust for your daughter both to protect it and ensure it doesnt affect her benefits

@WatchingTheDetective well OP has written that there is NO will!!