Agh, 2 1/2 hours to clear customs and immigration, wait for a bus, go round one of the busiest sections of road in the country at rush hour, check in, go through security and board?

That's seriously pushing it.

To be honest Speedlink (which I think has been integrated into National Express now) is as good a way as any - a taxi will not really be any faster, other than doing without the wait. But really, that is tight.