WorldPoints is the way to go!

You can save £14 right now. Go to www.baa.com/worldpoints and sign up. You'll get 100 points which you can cash in for 2 half-price HEX single trip vouchers. Note that these must be used at ticket offices at Paddington or LHR arrivals terminals - NOT on the train.

The easiest way to accumulate WorldPoints is to take advantage of their duty free offers. When you have joined, you can log on to the website and check the latest promos. For example, to the end of Feb, you get 250 bonus points when you buy three bottles of duty-free wine for £15. These 250 points can be redeemed for five half-price HEX singles - so you save £35 in return for spending £15 on wine!

If you get the BAA WorldPoints Visa you can also get a first class upgrade on the HEX - even if you bought your ticket for half price in the first place. You simply sit in First and flash your card when the guard comes round.

You can also redeem WorldPoints for BMI miles, at the rate of 500 for 750 miles. However, since 500 WorldPoints gets you £70-off 10 HEX tickets, you are better using them for train tickets.

PS. The HEX is actually the most expensive rail route in the world, I believe. And it is now £16 for a 15 minute journey if you buy your ticket on board.