Hi,
You'll need to shop around and ask for various quotes from shippers who have and can handle internationally for private house moves etc.
Unless the bunk beds have real sentimental value, I'd say not to bother shipping them, there's plenty of bunk beds available here. Clothing and toys are of course much more personal so perhaps quote for those only?
I'd also suggest you make a comprehensive itemised list of exactly what you want to bring and get quotes. You might be able to re-jig based on anything you decide you can just get over here.
Cheers, DtM! West London & Slough UK!