Perhaps they came from the nearby Parrot Zoo, now known as Lincs Wildlife Park.
It's just down the road and I believe they have had escapes before.
Just seen this below on their website:
Quote:
Parakeets
When visiting Lincolnshire Wildlife Park you will probably have a short panic when you see Parakeets flying around the grounds, landing on telephone wires and sitting on top of aviaries! Don’t worry… we know! We have approximately 30 Parakeets that fly freely around our park, they have nesting boxes around the Nature Reserve, The Rainforest Diner & at locations around the rest of the park. They have become so accustomed to their freedom that catching them to put them back in a captive environment would be very stressful for them and us. You will also see many species of Parakeet in our Walk-Through Aviary, where you can go in amongst the birds; feed them your millet bought from reception and let them use you as a perch for that great photo opportunity. Apparently it’s lucky to get pooed on so we take no responsibility for that… enjoy!