Thanks for confirming. Firstly, the legal position is that you have no right to occupy the property as you are not married and your name is ***** ***** the title. He is therefore entitled to request you leave upon giving you reasonable notice.
However, you have a few options given that you have two young children together. Firstly, if he is attempting to force you to leave you can apply for an occupation order to remain in the property due to you having children together. This order will exclude him from the property and allow you an the children to remain there but to obtain this you must demonstrate to the court that he is able to maintain himself elsewhere, whereas you will not be able to. This can be pursued using form FL401 to your local family court and should be used as a short-term solution.
In the event that you are unable to maintain yourself and the children elsewhere long-term, you can apply to court under the Children Act for the property to be held on trust for the benefit of the children until they reach a certain age, after which it returns to him. This can be done to your local family court using form A1 and a £255 court fee.
Furthermore, the event that you are made homeless, you can present as homeless to your local council housing office and if the children are in your care you will most likely be deemed in priority need and they can provide you emergency accommodation whilst looking at providing a duty more long-term.
I hope this assists you. If you found this information helpful please provide a positive rating using the stars at the top of this page. I will not be credited for your question without a positive rating. Thank you.