There's another alternative.  Reading - Paddington stopper to Hayes & Harlingdon and then the Heathrow Connect.  I did this recently from Twyford to Terminal 3 and it worked very well. Much cheaper too, about ^11 in middle of the day.

Not put off at all - an excellent discussion.  Based on the advice here I went to Twyford as usual to collect my tickets the day before and then caught  a direct Henley - Paddington train from Wargrave. (WGV is an unmanned station with no machine - it even has free parking so its not all bad).

I buy tickets on line and usually travel from Wargrave on the Henley branch.  Station is unmanned and there is no ticket machine. 

I usually drive to Twyford the night before to collect the tickets from there.  However a couple of times the machine has been out of action.  The alternative is to collect tickets at Twyford when I change trains but the connections can be tight and there is often a long queue.

So, can I just give the credit card I used for the booking to the train manager for the tickets to be printed.

I ask this because I recently collected some on-line tickets from the ticket office in Bath. As multiple machines were out of action a nice person printed the tickets for me.  He didn't need my booking ref. just the card I used and he was able to print ALL the tickets booked on that card.  Hence, can a train manager print the tickets for you on board the train if you join at an unmanned station?