Companies can, and do, develop HR policies which specify rules for relationships at work. But there is a difference from requiring staff couples to behave in a professional manner whilst at work, and banning relationships altogether.
This is bad HR practice - and only likely to make staff keep relationships secret. As for its legality however, this is another matter and there isn't yet any case law to follow. A policy this draconian may conflict with the Human Rights Act, which allows the right to a private life, even when at work. If you found yourself dismissed as a result, and you have 12 months' continuous service with your employer, you may have a case at an employment tribunal for unfair dismissal.
Sometimes a policy banning relationships may be defensible when used to protect against only particular types of relationships which might be seen as inappropriate or a betrayal of professional trust, such as between college tutors and students, or between doctors and patients. You should seek individual legal advice if you find yourself in this situation.
