Every computer built in the last 15 years or more will have a USB connector so I am sure it must be somewhere.
You don't say if it is a laptop or desktop, but look at the front and back of a desktop, plus round all the sides of a laptop. Make sure there is not a small "door" covering the connection.
The description of your 4 pins over 5 sounds like a DB-9 connector.
See picture below, is it like the top connector?
http://content.answcdn.com/main/content/img/CDE/DBCON.GIF
If so it is an RS-232 serial port but to be honest I have no idea if a modern printer would work through a old serial port.
You could try seeing if you can find a cable with USB A connector at one end and RS32 a the other.
Found this on a USA web site so you may be able to find one in the UK (but still not sure if it will work)
http://ppa-usa.com/computer-products/cable/usb-2-0-3-0/usb-to-serial-6-foot-cable.html