If a regulator really wants to get involved and is confident of Govt backing at a senior level (eg Secretary of State for Transport) and feels that alternative routes to solve the problem are ineffective, then they will get involved. A regulator that is perceived as ineffective (even if unfairly because it has no formal powers) may find itself with political problems of its own in the media or in Govt.
There are all kinds of ways the UK CAA can make trouble for non-UK airlines on an informal basis when on UK soil. While an airline can always challenge informal action through the courts, an airline may decide that modifying its behaviour slightly leads to a more positive outcome in the long term for the airline