Thanks for your question.
As you mother died intestate, her estate will pass under the intestacy rules. This means that your step-father will received her personal possessions and the first £250, 000.00 Anything over that will be split in two with one half passing to you and your siblings and the other half being held in trust with your step-father receiving the income until he dies at which point it will pass to you and your siblings.
Are you asking if you have a right to make a claim against your mother's estate?
Right. Your step-father will automatically receive those assets which were held jointly (as joint tenants) because of the rule of survivorship. However you do not know which assets are genuinely jointly held and which are not so it is certainly worth investigating.
You may very well be able to make a claim under the Inheritance (Provision for Family and Dependants) Act. It must be made within 6 months of the grant of probate or letters of administration. You will be applying the court for reasonable financial provision out of your mother's estate, there are a number of factors that the court takes in to account in deciding what is reasonable and you will need a solicitor to make the application for you.
Legal Aid is available for contentious probate matters such as yours would appear to be and you should call the Law Society on(NNN) NNN-NNNN1222 to ask for a contentious probate lawyer in your area with legal aid certificate. Get them to see you either for an initial free meeting or for a fixed fee.
Just because your step-father is saying he does not need a grant of probate does not necessarily mean this is the case and I would advise you to make a "standing search" of the probate calender, which will notify you and send you a copy of the grant if one is take out within 6 months of the date of the search:-https://www.hmcourts-service.gov.uk/cms/1211.htm
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