My father died intestate in 1972. how would I find out what I should have inherited ?

My mother has remarried twice and moved house several times. I understand she has a life interest in the estate she inherited from my father. How would I find out details

There can't be a life interest without a will, as others have mentioned, if there was no will, your mother would have got the entire estate.

The only knowledge I have in life interest wills is my own. The estate remains the property of our offspring but with control of the surviving parent until they die, co-habit with another or re-marry, it then becomes the sole property of our children.

There appears to be something missing from your info, you need to speak to a solicitor.

Don't understand about the life interest. If he died intestate it means he did not leave a will, so everything he had ie; property or money was left to his next of kin your mother. She can leave it all to anyone she likes when she dies. If she does not leave a will it will pass to her present husband.
If you think he did leave a will you can write to Somerset House in London for a copy.

How do you inherit a life estate without a will? 30 + years later?

I'd start by calling the probate clerk and making sure there either was a will or an intestate estate filed or not; I'd purchase copies of all estate documents; and I'd take the results to a good probate lawyer.

If your father died intestate, everything he owned went to your mother. You did not inherit anything

ask a lawyer