My own daughter was 2 when her father and I divorced. At that age, I'd not have wanted her traveling to another state, much less another country, for visitation. I'd have done my best to make sure he had to come and visit her.
He only saw her about 3 times in the next 3 years, and it really tore her up when he'd disappear. It took a toll, and they no longer have a relationship. She also has trust issues when it comes to men.
If you move to the UK and chose to visit, how frequently can you do so? What other means will you use to maintain your relationship with your daughter? At 2.5 years, they don't read or really use a telephone. Would your ex be willing to read letters or e-mails to her? How often do you think he would allow telephone (or Skype) calls? The few times my ex called, I had to participate in the phone calls, because of her speech. I also had to prompt her to say "yes" and "no," instead of nodding her head at the phone.
If your ex remarries or lives with another woman, your daughter will probably feel a bond there. This person would have a lot of influence over your daughter--especially with you being overseas. How well do you think you could handle this, especially from the UK. You say your relationship with your daughter is very important to you. She's in the years where some of the strongest bonding takes place.
My fiance left his two daughters with his ex...they are older 11 and 12 so he explained to them that he loves them etc...and then moved over to me. Since he has been back in the UK he hasnt seen them except on Fathers day...but they are kids so they are involved with their friends.
He made that decision. I never asked him to. He just decided. He has no visitation, and he is hurt that I haven't automatically made the same decision. But my daughter is younger.
It sounds like he chose to abdicate some major responsibility towards his children. Their age and having friends is no excuse. He could be a bigger part of their lives, and they could still see friends when it was time to be with their mother. They might even be able to make friends in his neighborhood. Have you considered having a child with him? Expect the same if the relationship sours afterward.
Does he have child-support obligations? Is he somehow honoring them without a job? If you go over there and get a job, will your income somehow be attached to any existing obligations of that nature? Would he expect you to use your earnings to satisfy any of these obligations? If so, you could be struggling economically more than you expect. If you and he have a child, and then break up, expect the same (priority, time and money) as he gives to his two current children.
Why are the 2 children this man hardly sees more precious than your daughter who you say you love and want to be with? This situation could easily breed resentment on your part over time.
No matter where you live as a couple, someone will spend a major piece of time away from his or her children. Who can deal with that more easily? It doesn't sound like that person is you, but he wants you to do so.
You have also indicated that this person has refused to take work because it was "boring." If he wanted you with him, he'd take whatever work was available to make it happen. Has he taken any real steps to get things set up for your arrival? It sounds like you've made the lion's share of the effort. Yet another piece of irresponsibility on his part.
While I understand that you have the right to pursue happiness, I don't see it happening for you with him. He doesn't seem to be actively trying to move things forward so you can start your life as a couple together. His disregard for one of the most meaningful things in your life (your daughter) is also deeply troubling to me. I wish you luck peace and wisdom, but could not leave my daughter--especially with the information you've given. I don't envy you your decision.