The circumstances you describe are likely to be seen as thorough explanation for you wishing to cancel the trip. Whether the airline will be sufficiently sympathetic to give you a full refund on a non-refundable fare is uncertain. Since the agent is not being helpful, you don't appear to have insurance and (if indeed this is the correct assumption) the tickets were sold as non-refundable or at least not in full, then your only recourse is to appeal to the airline directly. Try to go as far up as you possibly can - ask for the station manager at the London town office - and be as articulate as you can be, unemotional and calm as well. An airline is no less likely to see thir way to be generous where to them there is not an awful lot at stake (and there really is not) - you are not cancelling on a whim. Lots of people would say insurance should have been taken out, and they would be correct, but in its absence you are where you are.