score:4
You can definitely obtain a refund for the first ticket, from Tottenham Hale to Stansted, regardless of what ticket type you had - as you can obtain a fee-free refund if you decide to abandon your journey due to disruption.
As for the second ticket, from London to Cambridge, it's a bit trickier. You shouldn't really have been told to buy this - if there was serious disruption to trains from Tottenham Hale, ticket acceptance should have been arranged and you shouldn't have had to pay anything extra.
However, if there was no disruption to trains from London to Cambridge, you might still have an administration fee deducted from your refund.
In both instances you need to contact the company you bought your tickets from, e.g. the website/app or operator of the ticket machine/ticket office where you bought your ticket.
They might ask you to submit a picture of your tickets being cut in two (if you had paper tickets), but don't do this unless they actually ask you to do so!