Just to add something on the divorce side where things stand in the UK.
You see to think that you need to be separated for two years before divorce can commence. This is only one of the five reasons for UK divorce. Even once the two years is up, divorce has to be with mutual agreement so you could still be left stuck, and divorce proceedings would still take about 6 months depending upon agreeing the finances.
There are other grounds for divorce where the ball can be got rolling immediately. You can also divorce for adultery, which would not be straightforward, requiring proof or an admission. The more likely available avenue is divorce on the grounds of unreasonable behaviour. The definition of what is unreasonable is deliberately vague, and very mundane things have been used. It does create a adversarial setup, with one party accusing the other of something, and the other admitting or denying it. Co-habiting with OM would seem pretty unreasonable and would be relatively simple to prove once it occurred.
(Otherwise, if one partner lives separately for five years, they can be divorced without their agreement. The final one is abandonment, which also allow for a no-contest divorce)
One thing to remember with both filing on the grounds of adultery or unreasonable behaviour is a six month time limit, which once passed without action, creates an assumption of forgiveness.
The legal profession keeps mentioning the bringing in of no-fault divorce, but it's unlikely in a time-frame that would affect you.
It would benefit you greatly to consult with a family law solicitor to discuss your situation and options moving forward. For one thing, a legal separation might benefit you both, disentangling your finances, and protecting each of you from any financial mis-deeds by the other during this period of limbo. Costs a few hundred £, plus any legal costs, which you may be able to persuade WW to split with you as it may help you both.
You may also want to look at the ownership model of your home. See joint-property-ownership at the gov.uk website.
Most couple where both are on the mortgage are "joint tenants". If one of you dies, the other gets your share regardless of any will (which many people don't have anyway), which may be a factor if you are going to be separated for some time. You may wish to switch to being "tenants in common" so any share can be passed to children instead. Costs nothing except some solicitor time. You would still own 50% each.
It's very unlikely, but if you die before divorce, your WW inherits the property, marries OM as she's free to do so, dies some years later and OM inherits the property leaving your children with nothing.