I don't know what is considered 'big and heavy' with regards to packages but I've always found the US Postal Service to be reliable and cheap. I don't ship internationally a lot but I've shipped an ebay auction item to Germany and it was received inside a week. The rates are very reasonable too, with some flat rate boxes available (I think the largest maxes out at 20lbs though).
I don't know why everyone knocks the post office. It rocks.
Without knowing the exact weight and dimensions of you package, I can't give you a dollar amount. However, Excess Baggage Company claims to be able to get your package to London, England usually within 3-5 days.