Experiment...and see which gives you the most success.
Though, from my experience I prefer phone over email anyway. So I would always go for the phone and if she does not want to give me her number.....then obvouisly I did not make a big enouggh impression on her.
I do think that in terms of email the UK is behind the US in relation to general use and also you then the risk of being stereotyped as computer buff as its not as commonly used. I believe.