I am looking for 3 companies that provide warehousing for products,
and also the ability to instruct this company to ship particular
single item products to customers directly from the warehouse.

This term is called drop shipping, but searching for it has not helped me much.

Basically we want to send 100 different styles of t-shirt to a
warehouse in england, and them tell them to send a blue small sized
one to mary jones, and a red large one to bob smith etc etc

I believe the term used in England is Fulfillment Services.

Try the following:

www.cdl.uk.com
www.braywood.co.uk
www.pfsweb.com

Or search google for fulfillment + warehouse