Best bet Peter, is to replace the siphon. This means undoing the two nuts under the cistern connecting the siphon to the cistern and the pipe to the cistern (for which you will need gland pliers or similar) Switch of the water and catch water coming from the cistern in a bucket when undoing the nuts.
It sounds as though the plastic diaphragm is split and not functioning. If you wish you can replace just the diaphragm by threading out the siphon link (the S bit) from the pin and pulling out the mechanism from the bottom of the siphon. You can get either or both Siphon and diaphragm from the plumbers merchants, you will need two reels of ptfe tape too. Take the siphon with you so they can give you a replacement (the name means nothing to them) may be ten pounds or so..
Bucket head
December 2010