Hi OP, don’t waste any more time thinking about how you can persuade this silly man out of his plan for talaq. Focus on yourself and your children.
Lots of women have entered into a nikkah in the UK without realising they will not have any rights if there is talaq. You are not the only one. It is confusing, because the UK treats a nikkah carried out in some other countries like any other marriage, but not a nikkah carried out in the UK.
Many people around you - perhaps including your husband, or the imam who married you - will have known that a nikkah didn’t give you any rights under UK law. You should keep your anger not for yourself but for the people who knew what getting only a nikkah meant and didn’t warn you.
Under UK law you only have the rights of an ex-cohabitee, meaning very few rights, and it may be a waste of money to go to a solicitor. But it’s worth checking the situation with any property, bank accounts etc., in case you are named on them and can demand what’s yours. Contact a women’s group who can advise. You’ve been misled once by the people around you. Don’t let your husband mislead you now. Don’t assume what you have been told about your household money is true.
And you can most definitely claim child support for your children as everyone has told you, and you can also adjust your Universal Credit to reflect your new circumstances as single. You don’t need a solicitor to do that for you.
Regarding your Islamic rights, it might help to have someone who understands your community to advocate for you, to put across your side. If the imam and your community can make your husband understand his responsibilities, it may be easier to get him to help financially. You have done nothing wrong, and there is no Islamic reason for you to feel ashamed either. If anyone says you are to blame, that’s not Islam, it’s misogyny. Make sure you can prove talaq has happened in case you want another nikkah in the future, so make sure you get the paperwork as PP said. (And if you do want another nikkah in the future - with a much better man - insist on a UK registry office marriage as well, so your financial interests are protected.) Go along to the talaq meeting and hold your head up high.
As PP suggested, go to the Muslim Women’s Network. They can help you with all these issues and also help you think it through. Good luck!