@earthman, jrk is right, a 2013 1.2 has to be VVT and therefore interference - unless something very strange has been done like an earlier engine swop, not likely though.
I think a waterpump bearing failure would be the most likely thing, which could then throw the belt off if it wasn't attended to.
I'd much MUCH rather have a belt than a chain. Chains aren't universally reliable, I can think of 3 makes which are well known to give trouble at quite low mileages, and much more expensive to renew. Only ones I'd consider would be Honda and Mazda who do seem to have a reputation for longevity if a really good quality oil is used and changed regularly - I recently read an article stating that oil manufacturers are starting to produce engine specific oils for chain cam engines in a bid to increase chain life. By the way, although I prefer belts I'd be very reluctant indeed to consider a "wet belt" as used in certain Ford and Peugeot engines, Oh no siree Bob!
Your statement about taking a punt and replacing that O2 (lambda) sensor? If bad enough to blacken the tailpipe and give you "terrible" MPG then there would pretty much definitely be a fault code/codes posted for you to retrieve. I don't understand why you then slag off the diagnostic/electronic angle which could only serve to substantiate your findings and confirm you needed the sensor or not and possibly save you spending money you don't need to spend?