If its an ex council house that will have been the old clothes line poll, I removed ours abd it was a fair lump of concrete!.
Had to remove a few concrete wire fence posts as well ans again they didn't scrimp on the concrete!.
Yeah not ex-council, but it was one of those rotating washing line thingies, and they don't seem to have scrimped on the concrete either, sadly. I did dig down a bit, but gave up somewhere approaching 18".
The jack idea is really cute, but I'd need a big scaffolding pole or something, and I just haven't got anything like that.
I can't hammer anything down the inside of the central pole bit, unfortunately, as I whacked it a couple of times with the sledge, and it's all closed up. Not sure what I thought I might achieve really - probably just frustration. But the concrete didn't even vibrate when I whacked the metal seriously hard with the sledge...
Just for a laugh, I did manage to drill a few holes down into it with my ordinary old hammer drill and an 8mm masonry bit, and it did seem to penetrate reasonably well, so maybe I'll try making a line of them tomorrow, then try and break a big bit off with the sledge or something...
Trouble is, I haven't really got stone chisels to batter into holes, or metal bars to lever with or anything...