They also came quite close to succeeding, initially it looked like the Politburo would actually remove Soviet troops and let much of what they wanted to happen happen.

Then Khrushchev and the rest decided that if they let Hungary "go" they'd have a problem justifying to the people of the other not entirely willing Warsaw Pact countries why they couldn't also go.

(Dramatically simplifying for brevity), it was also a really bad time for it to happen because we (the British), French and Israeli’s decided to start a massive crisis in the middle east 2 days earlier which over shadowed events in Hungary.

My missus is Hungarian, god help you if you say that Hungary was in the USSR to her because no one else will.

Her family (and her father in particular) loathed the Hungarian Communist Party but he was something of an Anglophile which he passed on to her and indirectly that worked out for me, so when Hungary joined the EU/combined with the Hungarian government saying "If you don't like it leave" (summarising again) she decided to say "OK" and move to the UK.