If you use a UK sim in other parts of Europe you are roaming and therefore the cost will be greater. Most of the Uk carriers will have an international add on for roaming on a pay and go sim that you can purchase but the saving are to be made from phoning back to the UK from these countries and not to the US.
The cheapest option would be to buy a sim card in each country that you visit in Europe although this will mean having different phone numbers each time.
However, if you are going to be travelling for 2 - 4 weeks perhaps you could look into o2 UK's simplicity sim, this is a pay monthly contract for a minimum of one month (30 days notice required to end contract)and if you get the simplicity 25 sim (a sim only contract)you get the international travel service free, this can give you better rates but I suggest that you look into it more.
Here is a link to their website, have a look, I entered phoning from France to the US and the rates with international travel service was £0.35p per minute. You need to scroll down the page.
The best package for you - Untitled Page
If you are interested I suggest you contact them directly as sometimes o2 has a sister network abroad and the rates are the same as if in the UK.
International SIM
