The house is a matrimonial asset and you are also a legal co-owner. Your husband cannot sell it unless you agree or unless he obtains a court order. Same for you. The fact it is now paid off means there are no more mortgage payments so by moving out, you would not forego any rights to the property.
The marriage is not classed as a short one if it is more than 5 years, so a split of assets is likely as opposed to a clean break. There are two orders available: a clean break order (if there are no assets to split) and a consent order.
You can sell the property and that would give you each a fresh start. You can either apply for a judicial separation (and then a financial order), or a divorce (if you want to dissolve the marriage) and again, apply for a financial order. Bear in mind with a legal separation you remain married and as such no pension sharing order is permitted (unlike for divorce).
If you disagree and cannot come to an agreement, you can ask the local family court to assess a split of the finances and also to deal with the property.
Assuming your husband eventually agrees to a settlement then you can have a consent order drawn up to bind the parties to the agreed terms. The following company can draft the order and they also file it with the court too: Divorce-Online | Quick, Easy & Cheap Online Divorce From £59
The court will consider the factors contained within Section 25 of the Matrimonial Causes Act 1973 when it assesses a financial settlement. Therefore your ages, length of marriage, your earnings and earning potential (same for your husband) if you both still work, the assets including the former matrimonial home and pensions if applicable, any debts, financial and non-financial contributions to the marriage, your standard of living enjoyed before the marriage breakdown, your financial needs in future and your housing needs, any medical needs and so on.
The starting point is 50% but if there is a disparity in earnings or you have paid more in the way of mortgage, you can ask for more than 50% of the former matrimonial home.
It would be worth speaking with him to see if he would agree to any amicable agreement and a split of assets without having to involve the court. The more that can be agreed without the court's involvement, the better.
If nothing can be agreed then you would need to issue financial remedy proceedings once decree nisi comes through (if you start divorce proceedings), or obtain a decree of judicial separation, so you ask the court to become involved in a financial settlement as well as the divorce.
Before you involve the court with the finances you need to contact a local mediator which is compulsory before you ask the court to intervene in the financial aspect. You can find a local mediator here : https://www.familymediationcouncil.org.uk/find-local-mediator
Assuming mediation fails or your husband doesn't agree to mediation then you will need to issue financial remedy proceedings and you would need to complete and send two completed copies of Form A (available here: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/885814/form-a-eng.pdf) to your local family court and pay a fee of £255 payable to HMCTS. If you are on a low income or have low savings you can ask the court for help with the fee here https://www.gov.uk/get-help-with-court-fees
The court will then list a first appointment and give directions for a financial dispute resolution hearing (FDR) where the judge will give their opinion on a likely settlement - which usually prompts a settlement at this stage. The court will ensure the parties make full and frank disclosure of their assets and liabilities to ensure the financial positions of you both are known and to allow the court to make a settlement decision. If the case does not settle, further directions will be given and a final hearing may take place if neither of you can agree to settlement terms.
Finally, if you need money before the divorce finalises you can apply for “maintenance pending suit”, which means you ask the court for an order that your ex pays you support to help with bills and so on before the case finishes. You will need an application form under Part 18 of the Family Procedure Rules 2010 and the fee is £155. You would need to attend a hearing for this.