Tony Bryer wrote:
http://www.oystercard.com/use_1.php says that you can use an Oyster
card on "National Rail services in London ... You cannot use Oyster
for travel on mainline trains outside Zone 6 in London".

but

http://oystercard.com/buy_1_4.php#7 says "Pre Pay can only be used
on the following participating National Rail routes:" which does
not include the ones round here.

So if I understand right I cannot use my Oyster Prepay card to go
from Twickenham to Richmond on SWT and thence by underground. If I
pay the standard rail fare for this, then my Oystercard for the
rest I will lose out so I need to buy a one-day Travelcard from a
shop, which defeats the purpose of having an Oystercard. Or am I
missing something?

Yes. Don't use PrePay - buy an Oyster Travelcard, which is accepted
everywhere within the zones by TOCs. Last I checked, Twickenham was
within the TfL zones.