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!