Husband won’t make a will

Flugelhorn

he sounds like he has his head in the sand.
if you own the house then they have no claim on it, if his total estate is under 270 then they can't claim anything. 
i wonder if your other half is aware that they will be left nothing?  - that may encourage him to do something 

Malthusian

Even if he makes a Will the younger children would have a decent chance of an Inheritance (Provision for Family and Dependents) Act claim on his estate if he left them nothing, as he is paying them maintenance. Is he in England / Wales?

There is however no possibility of the house being sold if it isn't part of his estate.

Book a solicitor's appointment on Valentine's Day and a romantic meal for afterwards.

TBagpuss

Owain_Moneysaver said:

jacksprat27 said:

He has 3 children from a previous relationship, 2 of them under 18 and provides maintenance for them. 

Are you a legally-recognised adoptive parent of those children? If not, and he doesn't make a Will, then the Court will have to appoint a Guardian of his children. That might not be you. If he would prefer it to be you (or he is emphatic he doesn't want Wicked Aunt Edna to get the children) he needs to make a Will. 
Not making a Will is a great way to say to his children "I didn't think you were worth an hour of my time with a solicitor". 

That's not correct unless their mother had also died. 
If he would want them to live with you if both he and their mother died, then yes, he needs to make a will, or a separate written appointment of a guardian.
In terms of your financial position, as others have said, his ex or children would have no claim on a house in your sole name, and if he doesn't make one, you will be entitled to the first £270,000 of his estate but his ex could potentially apply for provision for the children, and he may want to arrange something so that his children get to know that he thought about them and made provision for them.