Aha - I just googled, and in the US 'parakeet' is used to refer to what I would call a budgie. I don't mean those, I mean a larger, bright green bird, like this or this. I didn't notice whether they had a ring neck.
They have obviously survived the harsh (harsh for the UK) winter. I saw one or two flying up to a hole in a tree and putting their heads inside, so I think they were feeding chicks. There were several flocks of about a dozen each. I wonder if they shelter inside the hollow trees when it is very cold.