It *does* sound like the connector but rather than pay out for a new one and find it's not that, it's probably worth trying your iPod and dock/connector on another computer first. If you know anyone else with a Mac, or PC with FireWire port, perhaps you could ask them if they could help.
Alternatively, you could take your iPod and dock/connector to an Apple dealer to see if they'd try them out for you to identify the cause of the problem. There are several dealers in London - the Regents Street store (which is a full-blown Apple Store) is most central.
Keep us posted.