Jimbo
When your wife receives her British Passport she will also have her Philippine passport. Means she can travel anywhere on whichever she chooses. She may choose to leave and enter UK on her British Passport and enter and leave Phils on her Phil passport. Both remain valid travel documents. But in principle of law she no longer retains all the legal benefits and privileges of Philippine citizenship.
However, she may decide to apply for Philippine citizenship retention/reacquisition.
This entails going to the Philippine Embassy in person in order to take the oath of allegiance and receive her certificate.
Be prepared that her current Phil passport will be cancelled prior to her oath taking and she will be asked to apply for a new one. I suggest that this would be advisable. So be prepared with photo’s and documentation.
When my wife did her oath taking we were not aware/prepared for new passport application and had time constraints anyway.
My wife still did not yet renew her Phils passport although we have visited the Philippines.
If your wife decided not to get her new passport she would need to take her Certificate of Oath of Allegiance as proof of Philippine citizenship when entering the Philippines. If you enter together you will still be able to have balikbayan stamp. Your wife will enter on her British Passport. The Certificate of Oath of Allegiance is not a valid travel document.