They can't but they can stop Ryanair from operating in the UK.
No I don't believe Ryanair can be stopped from operating in the UK. My limited understanding of their authority however is that they can fine Ryanair for every passenger they carry in the UK. This of course is post all the legal wranglings and appeals. I could be wrong on this but I think that this is the procedure they use to enforce their ruling. I wouldn't anticipate it going that far though. The appeals process could take up to a couple of years with the law firms dragging it out for as long as possible and licking their lips.
Ultimately I see Ryanair selling their share before an appeals process runs its course should an investor make a satisfactory offer for part or all of their shareholding. When will then happen is a huge fanfare with the usual rhetoric of Aer Lingus as an airline is doomed etc etc will take place for a few days. After that the event will be forgotten and life will carry on as normal for both airlines.