LOL, looks like you have now learned about the stage of Flaking. This has nothing to do with England or whatever part of the world. It's simply a reality of cold approach.

While your approach might be solid, there is a natural rebound effect when those good emotions of your interaction wear off. And builds her own internal resistance to continuing an interaction with you. Such as thinking are you safe? Does it mean she is easy? So this is normal.

One thing that might help with flakes is exchanging Facebook or instagram contacts. Although I'm sure getting a phone number feels more "official" and like you closed on something. But the objective is not to get numbers, but to build a connection that leads to something romantic. So its a means not an end. I mean often when you get a number, usually you just text back and forth for a bit. And most people have their facebook or instagram app loaded on the phone anyways so they get messages instantly. These days very few people make calls.

Part of the rebound effect I think that comes from cold approach, her sense of logic comes in that you are a stranger. And she doesn't know if you are a psycho killer or just some lonely loser who put up a good show for her. A facebook contact shows more familiarity about who you are and who she is. She can then see things about you that you are a regular cool guy. And who knows might even know mutual people (That can be a good or bad thing). Plus you can now do voice and video calls via facebook as well. So actually gives you more opportunity to communicate than a phone number alone.

Give that a try and see if it helps any.