storage fees with shipping companies (US to UK)?

I'm moving to London from NYC in Sept with my husband, and we've got an opportunity to sublet a furnished flat there 'till December. The thing is,  our stuff will arrive earlier -- October-ish?-- and I'm wondering if we'll be hit with huge storage fees?
Does anyone have this experience? It's not so much stuff-- small NYC apt life.

I'm sure it's worth looking into storage businesses as an alternative to just leaving your things with the shipping company.