I am largely in the same camp as other women on this thread that I think it's on you to sort. But, let's accept it's happening and you are moving.... how can you manage this to be less detrimental. For a start, the detriment you have to focs on here is your DD - so how do you minimise impact on her?
Are you actively involved in her life currently? Becuase if not, this is going to be even worse. Let's say you are. She's 12. So old enough for a phone. Which means you need to be proactivel engaging with her. Send her pictures and memes, call regularly. But no pressure. Don't be having meltdowns because you called and she didn't answer ror only spoke for a few minutes. IN real life parenting, most of the time our interactions with our DC are not deep meaningful chats of an hour, but in passing chit chat while making breakfast, driving to football, as they come trhough the door from school.
Make sure you stay current on what's happening at school. Stay on email distribution lists for newsletter and parent info. READ IT. Pay attention - if she has a test, ask her how it went. If you're good at maths, can you help her with her maths homework remotely? If she's practicing for a dance show, can you facetime to watch her practice? Whatever works for you and for her.
Visit as often as you can. Sorry, but easter and Christmas isn't good enough. You need to make more effort to get over here more frequently. 4 hours isn't insurmountable. Make sure you're here for that major match when her team is in the final, turn up for the school play, come over for parents evening, don't miss her birthday.... etc etc And yes, this will be expensive. It's important though so prioritise it.
When you're here. Don't isolate her. Yes, you want to see her but that doesn' tmean she should have to cancel her football training or attending her BFF's birthday party. Drive her around, spend time with her between, plan fun activities between.
Oh, and continue to pay. Reduce friction between you and your ex by making sure you're meeting your share of the financial obligations. If you can, treat her when you have her (even if those treats are agreed with your ex eg new coat, new shoes, phone etc) Don't bad mouth your ex. Don't badmouth England - this is where she lives.