He did end things with her ( I know that for a fact)
With respect, @Strawberrina, you aren’t there with them, so you cannot definitively know this.
Many adulterers lie about ending their infidelity to keep their marriage/home comforts/money and their mistresses. Your H has positioned himself in the perfect set up for a continued double life. He has experienced zero consequences to motivate him to make real changes.
If he is in love with OW and is still working closely with her everyday, then the affair is continuing. Their mutual affection, ego validation, physical attraction, emotional bond and reliance, in-jokes — it’s all still there. His love for her is being watered and nurtured by their close proximity on a daily basis.
How long had the affair been going on when you discovered it?
As the injured party, you have the right to set both consequences for his betrayal and requirements for reconciliation. It’s not too late, as you have agency and options.
You can:
*tell him you’re reconsidering the reconciliation and need space
*require his NC with OW
*require his changing jobs
*require CC as well as IC for him
*require open access to his phone, devices and statements
*consult with a solicitor to get information
*access IC to gain clarity and strengthen your self-esteem as you make decisions
Or, you could go ahead and file for divorce (I would) because of his heinous disrespect and disregard — not only via his original betrayal, but also by his subsequent failure to completely cut off his affair partner whom he admits being in love with.