Hi Paul,
If I play at home late at night it has to be quietly to avoid disturbing the neighbours.
Using tin or Shaw whistles I can play the basic melody of a tune at minimum damage level by keeping each note as short as possible. No good for learning a peice properly - but I can at least start to learn a new melody or work on a rhythm.
I've used headphones/keyboard to learn a new piece, again not proper practice but it helps with learning the tune/rhythm at least.
When I first starting playing - I'd play in my car to avoid being hear at all.
I've seen guitarists advised to quiten their instrument by tucking a hanky under the strings - I don't think a hanky stuffed up a whistle would work. ( & it's too late to try it now !)
Don't suppose there's a shed/annexe/boiler room ? Or a room next to woodwork/metalwork class ?
Good luck !