Financial infidelity is a real thing.
Personally, I would divorce her and tell her I want the 7k debt to be deducted from her half of the marital assets (idk about UK but I think here she would have to agree to that because debt, like assets, is considered shared equally in divorces). If you want to try to save the marriage, I would tell her the terms include immediate marriage counseling, immediate financial counseling for her, and that she gets a second job or picks up hours at current job to pay the entirety of that debt herself.
Happened to a buddy. He divorced her. He’s now very happy.