Re: islamic will…
If he writes a legal will under UK law with witnesses and all, and specifies in his will the exact manner in which his property is to be distributed (rather than just saying “islamically”, he should say what share and exactly what goes to whom), then the wife cannot overrule it, just as a spouse cannot overrule any Christian’s will. If he writes a legal will and excludes you from it… there’s nothing you can do.
However, if he dies without a will, expecting that things would be shared according to Shariah, then there is a worse problem and any of his potential heirs (siblings, cousins, uncles, aunts, etc) can lay a claim on his property.
The main benefit of getting legally married is lower capital gains tax (it can be split between you and your spouse) and zero inheritance tax when inheriting your spouse’s property.
The website at this link specifies the following disadvantages to not being legally married.
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Your husband would legally not have parental responsibility. PR is defined in the Children Act 1989 as ‘all the rights, duties, powers, responsibilities and authorities which by law a parent of a child has in relation to the child and his property.’ Without it, he doesn’t have any right to be involved in decisions such as where the child lives, their education, religion or medical treatment.
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You have no legal protection under UK law should he leave you. Without being married under UK law he could just walk out and is not responsible for giving you any financial support.
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if you are not married or not in a civil partnership you may find that hospitals and other such official bodies do not accept your involvement in the affairs of your partner, however long the relationship. These bodies will give more recognition to married and civil partnered couples.
Most medical practitioners will be sensitive to the issue and will understand that, should you need medical treatment, you will want you partner involved, whether you are married, civil partnered, or not. It may be helpful to have a document stating that you would wish your partner to be consulted and involved.
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The website I linked to gives a lot of information on this topic - from the UK legal perspective, it should be all you need.