In the right situation 'swallowing a balloon' is a very entertaining routine, especially when entertaining adults. I do not consider it appropriate when entertaining children. What is the correct technique for achieving this?

Swallowing a balloon is a magic trick that many magicians have published. It is not fair to those magicians if we just give away this method. The most recent i believe is deep by justin meitz.
 It is kind of like saying "walking through a wall is a great effect, how can i achieve this?" This is not fair to the person who came up with that effect. If you are interested in who did first publish the walking through a wall effect, it is not known for sure, however most think it was an egyptian man. If you are interested in purchasing it, the effect is called "a door"

The balloon swallow is, like you said, a very powerful trick. Not great for kids especially if you are doing balloon animals after, they will all try to copy you!!!

There is an interesting thread on the magic café about the balloon swallow and Justin Meitz, they say this effect first appeared on a DVD by Steve Bedwell .
Steve was a Doctor from the UK but now I believe he lives in the US. The idea was taken from a street performer in the UK.

There are plenty of places to learn the effect and the rage will go on about if you should perform the effect in front of children.

Many thanks for your help and views on this. I will follow up the Magic Café thread.

Kind regards

Robin Maddy