No, that is not the case.
You may have gotten confused because often a financial consent order will say for example that maintenance stops being payable if the person receiving the payments cohabits for a period of 6 months or more. Some consent orders will say that a property is sold on cohabitation but this is less likely because cohabitation isn't really going to affect the ex-spouse's or children's accommodation needs.
So what happens now? Well, if your estranged husband is not bothered, nothing. If he is bothered, easiest thing for him would be to petition for divorce on basis of 5 years separation and make an application for a financial remedy. This may or may not result in the house being sold and proceeds divided. Depends on a variety of factors (if you look at section 25 of the Matrimonial Causes Act 1973, it tells you the list of factors taken into account).
As you both have new partners, it might be an idea to divorce and get the finances resolved. As it stands, if either of you died without a will, the other would inherit which might not fit with your wishes. If things are amicable, you could go to mediation to get an agreement, pay a solicitor to draw up a consent order and provided that you are reasonably comfortable with form-filling and legal documents, you can do the divorce petition yourselves to save costs.
If I were you, I would pay for an initial consultation with a solicitor though (they are unlikely to cover enough in the free half hour appointments offered). When I was in practice, I used to do them for £175 plus VAT and see the client for up to two hours and then write a detailed advice letter. That can then help you if you go to mediation, as you will have the legal position clear in your head.