Hi carofr,
Welcome to askaboutmoney.
Irish and UK law may be similar but they are not the same.
As Vanilla says, you should seek advice from people well versed in UK law.
Whoever you talk to, you need to differentiate between adoption and becoming someone's step daughter.
If you're adopted, normally you are related to neither parent by blood, but are wholly related to them by a legal adoption.
A step daughter may be related by blood to one parent but to the other through the blood parents subsequent marriage to the other person.
This is a simplistic explanation, and there are several combinations and permutations in a society which may practise sequential monogamy and divorce.
I don't know the succession rights for a stepdaughter here or in the UK.
In Ireland the adoption laws confer absolutely the same succession rights for adopted children as those who are blood related, even when there are both in the same family.
Consider speaking to a family law solicitor in the UK to get further clarity on this, and perhaps ask them to check what happened to the proceeds of the disposal of your mother's assets.
The "daugher of your mother's sister" is your mother's niece and your cousin.
She may have few succession rights in comparison to you under normal circumstances in the UK.
Succession rights may or course have been determined by the will of deceased relatives and the wishes of living ones.
ONQ
All advice on AAM is remote from the situation and cannot be relied upon as a defence or support - in and of itself - should legal action be taken.
Competent legal professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matters at hand.