The company automatically calls you back in your hotel, and it's recorded as an incoming call - that means no surcharge. Now, you have an open line to dial any number, any where. Check out kallback for more details. Even if you deal with a nationally known chain that has a branch overseas, the system doesn't necessarily work the same way. Just because you have a voucher for a reserved car, it doesn't mean you have a reservation.
Companies overseas operate as an independent.
To insure there's no mixup, invest a little money and call the branch in the country you're visiting to confirm. There may not be any discount tickets between New York and your international destination. So, once you get to London, make your plans to country-hop FROM London.