There are any number of taxi services in Reading and it's easy enough to find one on the Internet…read morethat is happy to take you to Heathrow. The challenge is finding one that doesn't charge an arm and a leg. Abbey Cars gave me a flat rate of £40 for the trip to Terminal 4 so I booked it.
The driver arrived a few minutes early and in a Mercedes C class, no less. That's not the usual treatment, I learned, but I have no complaints. He was polite and professional and a decently good driver. We got to the airport in record time and I made my flight with plenty of time to spare.
Would I use Abbey Cars again? It's difficult to justify £40 when the Railair shuttle charges £17, but with the amount of luggage I had on that trip it was worth it. Especially since Railair only goes to Terminals 1, 3 and 5.