Thank you! I should have waited until you replied lol I sent an email as I knew the deadline was tomorrow. If they reply I can then seek clarification and I really appreciate your help, that makes sense! At least I don't sound too bad and I said at the end if there are any issues let me know so they can always come back saying they don't do it!Since you will be replying to their email anyways with dates and times for your travel already, maybe in there add a section asking for clarification and explain that you will be commuting into London daily and as such ask if they would be willing to buy you a weekly travel ticket so that all of your journeys for the scheme could be covered, that way it would also be cheaper than buying a ticket for each individual journey and you will be able to take the train at any time of day which will be useful if you go to a Vac scheme social or stay in the office later than usual
Definitely ask for clarification and even if you ask them to pay for all of your travel I don't think that would be seen as cheeky, firms have lots of money and you should take advantage of that lol!