Try this web-site:http://www.mutr.co.uk/
They have solenoids under "Electronic Components" and then "Solenoids and Relays". But they seem a bit expensive?
There's probably a downloadable PDF with the specification of the Farnell parts, which should show how the pull/push mechanism works. Most solenoids will "pull" magnetically and then use a spring to return to the "off" position. You may need to use "pull" solenoids and a simple lever arrangement to get a "push".
It's quite normal for the moving part of a solenoid to be free to fall out! They're intended to be used within a larger mechanism, and that will hold the plunger in place.