I have been aware for some months of a relationship between two of my staff. They were discreet and caused no offence and so I thought nothing of it. However, this relationship has now deteriorated. One of the pair has found another partner (thankfully outside college) which is causing a great deal of acrimony. Other staff have complained about the atmosphere and I have witnessed a very ugly scene in the cafeteria. I feel that I really should say something.
And so you should, but tactfully. Point out that their behaviour towards each other will obviously impact on others. A staff-room or office away from the classroom should be a place of calm and of course a place to bemoan the latest quick-fix idea from Number 10 and anything else that rankles. Workplace relationships are generally a bad idea but you can't stop colleagues having them.