There's a few companies out there who offer a US address for you to order to, and they'll then ship from the US, so you can order from US firms online who don't ship internationally (the big lamers).

Anyone have any experience of one of these services? There's a few bits and pieces I need for the car and it would greatly expand my potential parts base.

Have you tried contacting some of the parts suppliers directly? Some will ship outside the USA.

Otherwise, I've always used friends in the USA to buy the stuff for me and send it on.

I have to agree, contact the supplier many will deliver to the UK. If not then ask a friend in the country if they can accept delivery for you and then forward for you. I have done that quiet a few times. It also helps if you do not have a Nigerian name.