Are there turnstiles at Twickenham Station exit?
I can see your point. The amount of times I’ve boarded a train with a valid ticket and nobody has ever asked to see it; be it on the train or at the station. And it really does piss you off abit. The problem you have is Twickenham. I believe from memory it does have ticket barriers, which would cause you a problem if you have no ticket. The cheapest way to do it would be to take the Tube on the District line to Richmond, and then buying a ticket from Richmond to Twickenham. The entire journey would cost £4 on the tube and £2.10 on the train. You may not even have to pay for the tube if you include it on your £20 ticket. Alternatively, buy a ticket from Richmond to Twickenham from any ticket office around the UK, and then fare dodge between Waterloo and Richmond, but at least that way you’ll have something to get through the ticket barrier with. And that’ll only have cost you £2.10 instead of £10.