Estimate of costs to ship a 2 bedroom apartment from New York to London?

I would like to know how much it would cost to ship furniture and household goods from New York to London. Our apartment has 2 bedrooms and a living/ dining area and we would want to bring all our furniture. We would also want the movers to pack for us. The moving companies all say they need to come out to our home to see our belongings to give an estimate, but I just want a ballpark - would it be close to $5,000, $10,000, $20,000, more?