From the NHS Website,
"When to self-isolate
Self-isolate immediately if:
you have any symptoms of coronavirus (a high temperature, a new, continuous cough or a loss or change to your sense of smell or taste)you've tested positive for coronavirus – this means you have coronavirus
you live with someone who has symptoms or tested positivesomeone in your support bubble has symptoms or tested positivey
ou're told to self-isolate by NHS Test and Trace or the NHS COVID-19 appyou arrive in the UK from a country with a high coronavirus risk – see GOV.UK: how to self-isolate when you travel to the UK
What is a support bubble?
Information:
If you think you've been in contact with someone who has coronavirus, but you do not have symptoms and have not been told to self-isolate, continue to follow social distancing advice."
The girlfriend has to self-isolate because someone in her "bubble" is positive.
No-one in your household need isolate since the girlfriend is not positive.