About 14 years ago I was found guilty of drink driving.

The sentence was £200 and 80 hours of community service.

I paid the fine and completed about 30 hours of community service.

The reason that I know a warrant was issued was because I was in the UK at the time, I appeared at the entrance of the court about 25 minutes late and heard my community service officer say "issue a warrant".

This was 14 years ago.. I have lived in the USA for nearly 13 years.

My Father is now not well and I need to return to the UK.

What are my chances of getting picked up at the airport? That could totally screw me, I would have issues seeing my family and am also concerned about being able to return to the USA in a timely enough manner to resume my work.

Thought... Maybe I would be better flying to Dublin, Amsterdam or maybe even into Paris and entering into the UK by ferry or train?

I doubt they would be actively looking for you, but you never know, they may get you for some entirely unrelated issue and find out you have a VERY old warrant I suppose.

Probation violation is hardly a high priority.

Taking a train or ferry from Ireland or the continent won't necessarily allow OP to evade detection.

I would contact a lawyer in the location where OP thinks the warrant may have been issued, and make arrangements for it to go away.