On our last few trips, since we are a family of 4 with a moderate amount of luggage we have used a driving service. The fare is not too out of line with using public transportation once you pay for four. Compared to taxis they offered a great price. Plus they are there waiting for you.
The link is:
http://www.airport-transfers-uk.com/index.html
We found the drivers to be courteous, friendly and professional. We also hired them to drive us to and from the port of Harwich a few times. I compared the cost to other providers and this service was reasonable. Most of all we had peace of mind using them. There were no surprises and they took great care of us.