AFAIK the Consulate/Embassy are not there to organise you flights or deal with expenses you have incurred with your own stupidity. They won't get you out of jail either, or take "sides" if you are having an argument with the authorities. They will also very reasonably expect you to have travel insurance which would take care of many events overseas.
They are there to advise on paperwork like getting this baby a passport and this is what they are doing by ordering the DNA test. Once that's through, they will organise the passport. They will also do things like visiting Brits locked up in an overseas prison to make sure they are being treated humanely, or advise on things like English speaking lawyers or doctors.
So many people think the Embassy or Consulate is there as some sort of 24 hour 7 day a week problem solving service, sort of a cross between MoneySaving Expert and Rip off Britain, free of charge of course.