2 for 1 in LONDON

You cannot use 241 with Oyster. It is only compatible with paper Travelcards purchased from mainline train stain stations (not tube office ticket boxes). You cannot use the tickets from LHR as LHR is not a mainline station although Heathrow Connect runs out of LHR so I could be wrong)

Each day you use 241 you need the Travelcard. Buy Travelcards and do ToL and The Globe in one day and Legoland another day but you must have Travelcards for both days. Any day you want to use a 241 you must have a Travelcard.

Do check that 241 deals are cheaper than a family tkt.

Mark is correct - you cannot use 2 for 1 with Oyster, only with rail tickets (which includes travelcards) bought at a mainline station

As you are around for 2 weeks you may wish to consider weekly travelcards which if you travel every day will be cheaper than daily ones.

"As you are around for 2 weeks you may wish to consider weekly travelcards which if you travel every day will be cheaper than daily ones. "

Just to add that for 7 day travelcards (not the 1 day) you need a passport sized (not quality) photo for each persons card.

#3 you do not need a photo for a 7 days travelcard, only for monthly and annual travelcards.
Regarding the general question of getting a rail ticket for the 2 for 1 offers.
1) some Heathrow terminals have counters selling rail tickets and it may be possible to get a rail ticket from them, a Travelcard purchased from a rail company will work for the offer whereas the exact same Travelcard purchased from the Tube will not.
2) My experience has been that most of the cashiers at the ticket offices of the places offering the discounts never ask to see your rail ticket.
3) If you do have an Oyster Card or a Travelcard purchased from the Tube, you can always find lots of used tickets dated today on the floor of major rail stations, there is a lack of waste baskets (the IRA used to like to stick bombs in them).

If you do have an Oyster Card or a Travelcard purchased from the Tube, you can always find lots of used tickets dated today on the floor of major rail stations

That is untrue since to clear most (all?) major station turnstiles you lose the ticket. Maybe you'd find one but the idea of 'lots' is wrong. And many stations have the clear plastic bag hanging from hoops which serve as bins.

"#3 you do not need a photo for a 7 days travelcard, only for monthly and annual travelcards."

Oh yes you do:
http://www.londontoolkit.com/blog/transport/photocards-now-required-for-7-day-travelcards-purchased-from-railway-ticket-offices/

#6 Sorry, while you do not need a Photocard for a 7 day Travelcard bought from the Tube or a 7 Day Oyster card travel pass, you do need one for a 7 day Travelcard bought from National Rail (since May 2012), the only thing I can add is that while management have introduced this restriction they have not done a great job of communicating the change to customers or staff. A friend often buys 7 day Travelcards from a National Rail ticket machine and did wonder when it started to ask for a Photocard number last year but they just typed 123456789 which is printed on the Travelcards, which have been shown to ticket inspectors many times and nobody has ever said anything about it.
To the OP, if you cannot buy National Rail ticket/travelcard at Heathrow the closest National Rail station is Feltham, a mile or two south of the airport, buses go there from Heathrow Central or Hatton Cross bus stations, and it has fast trains into Waterloo.

you do not need a Photocard for a 7 day Travelcard bought from the Tube

Correct, but it will be on an Oyster card if bought from the tube.

I live on the outskirts of London and use 241 to sightsee - I cant remember the last time I was asked to show my train ticket when using the voucher - so you might also get away without showing one, but this is a gamble.

Although if you were to take the children to see a 241 show, I doubt very very very much they will ask to see the train tickets when you arrive at the theatre (they never have for me) but again I cant say with certainty this will be the case.

Ive had a look at the FAQ section on the website and it doesn't actually specify journey lengths in relation to eligibility - it just says the train tickets have to be National Rail, and they have to be into London.......so maybe you could buy 4 tickets from say Stratford to London (overground National Rail) at any station, and use these to get into the attractions on 241? You might be able to get group save (buy 2 train tickets get 2 free or something similar) which would still make the saving on the 241 attractions worthwhile. It also says a single ticket into London is sufficient to use the 241 attarction voucher......

If you want I can go ask at the train station? I live close by and dont mind helping out with the reasearch as payback for all the other people that help me out on here :-)