it would just affect the ehu box you are hooked up to. sometimes this can affect the other ehu cables attached to the same box but not always. site warden usually has to come and open the ehu box and press reset button.
Most EHU circuit breakers are 10 Amp, so would be likely to trip. You would be snookered on a site with 5A electrics - there are a few of them, especially abroad. We use a 750W travel kettle from Argos.
I use a normal household kettle (but never at the same time as anything else, except maybe the TV) and have never had any problems - but then I've never been on a site with less than 10amp.