Rights following parent death

Hello. I am hoping someone can help me make better understanding of my rights following my fathers death.
My father died a couple of months back leaving us four children, and his partner of 20+ years.
My father had been with his partner for 20+ years, they did not marry, however she legally took on his name. They have no children together, however her children and grandchildren did call him father/grandfather.

My father had four children, his first born is no longer with us and I am the youngest of his three remaining children.

Our relationship with our father has been a on/off relationship ever since he started his relationship with his partner, and nether of us have had much to do with our father over the years despite living in the same town. The reason for this is simply because his partner never really wanted us around and made having much of a relationship with him very hard. We kept in touch and would always be the first ones contacted should his poor health land him in hospital over the last few years, on his orders we were always contacted.

My father died having had a heart attack which then led to him being in a coma. His children were told of his ill health only on his death, despite him being in the hospital for a week up until he died. News of his poor health, the fact that he was dying was kept from us and was a decision made by his girlfriend.
News of my fathers resting place, chapel of rest and funeral arrangements was also kept from us, and a message was sent via a relative of her’s that we (dad’s 3 remaining children) where not to attend as there would be no welcome for us.

Our father always told us that we would come into inheritance after his death, it was something that he repeated many times over the years.

The issue I have is “I have no guarantee wether there is a Will or not”, and I have been unsuccessful in finding out. I did go a speak to a solicitor who said that “if there is a Will then she will be in charge of that will and we have no option but to wait and see wether a Will goes in for probate”. The solicitor did send a letter on my behalf and asking for a copy, but like I expected ‘I’ve heard nothing from her’.
I understand that all I can do now is to wait to see if a Will is put forward for probate.

What I’m struggling to understand is “what happens if there is no Will?”, as we are unlikely to be told of this, and at present his partner is busy selling all of our fathers possession’s and is taking her entire family abroad, basically living the life and we have no way of knowing how her new lifestyle is being funded. His possessions and now his car have been sold, but has she actually got the legal right to do this as they were not married and his three remaining children are his only living blood relatives? I’m failing to understand what right I have, if any, and what should I be doing about this. I,’we’, are in limbo and have been kept at arms length and have been left being told nothing. Can someone please explain to me what rights she has?, as his girlfriend of 20+ years, and if infact there is no Will, then how are we to know wether we have a legal right to what he did have, should there be anything left to be had?

Thank you