ITIN for US work?

Hey folks,

Can't believe it's taken me so long to register here, and to open with a numbers question! Brilliant community!

Anyway, my question is this - I'm set up as a designer in the UK (sole trader) but I'm on a retainer and do the vast majority of my work for a US based company. They've asked my to fill out a W-7 form and get an ITIN number but I'm not convinced I need one - given that I'm based in the UK, registered in the UK and invoice from the UK, should I need to deal with the IRS at all?

I called the IRS directly (luckily I have free international minutes) and the helpful guy on the other end said that the US company didn't need to file anything for me but the company I work for is still unsure.

Anyone with experience of this sort of thing? Any advice much appreciated!