I was justifying to my Sunni friend why as Shia Muslims we look for the moon in our own country to declare Eid to be the following day. She asked what we do if it is too cloudy to see the moon, as for example we live in England and it is often cloudy. I didn't have a response to this. Could you please give me an answer to this?

If it is cloudy and there was a possibility of sighting in your own country (according to published knowledge) then according to A. Sistani, a sighting in another country can be followed.