Rotary washing line - pole snapped

The pole of our 20 year old rotary washing line snapped yesterday about 2 inches from the ground. All that is left is the plastic sleeve that is concreted into the patio and within that the base of the pole. I've tried to remove this piece of pole from within the sleeve but it is stuck fast. So, what are my options?

Doubt if a new pole will fit unless the pole is a smaller diameter than the original one. My thinking was to buy a pole which has a spike on the bottom designed to go into a lawn and as this is tapered I may be able to force it into the sleeve enough for the line to be sturdy. The other option is to remove a few slabs, dig out the existing sleeve and concrete and replace it with a new one but this is really more work than I'd really like to undertake.

Thoughts?

Can't you buy some metal rod that fits the ID and use this to re-attach both parts. Chop out the rusty bit and blather the inside with acf50 or similar.

I like this idea although I would wonder whether the whole structure would be a little wobbly unless the new tubing was a tight fit.

If the sleeve does come out, just stick it back in again.

It's got to be worth having a more serious try at extracting the broken end. Soak it in penetrating oil and try tapping it round with hammer and cold chisel to loosen it, for example. Then yank it out as above.

I've had this exact same thing, twice now. No point in trying to reuse the socket, even if you can get the rusted, snapped bit of pole out. They were both cheapies.

Dig a 30x30 cm piece of the turf out, and a further hole around the socket to the concrete base. Angle grinder to cut the stub off.

The new Brabantia whirlygigs have a much more robust ground spike which really doesn't need to be concreted in. I was sceptical but they are really strong and solid once driven in. Much thicker, aluminium pole too.

This is the one I replaced them with

Brabantia - Lift-O-Matic - 50 Metres of Clothes Line - Adjustable in Height - UV-Resistant & Non-Slip Lining - Umbrella System - Rotary Dryer with Ground Spike 45 mm - Anthracite - ø 295 cm https://amzn.eu/d/4EMVbQ2

Penetrating oil for a while. Then grip it with mole grips or those pipe grip things and twist it from side to side. Once it starts moving, keep twisting and lift at the same time.

That's how I got mine out in the past.

Thanks for all the replies.

I managed to remove the end of the pole by using a claw hammer similar to how you would remove nails from a plank of wood. Unfortunately (fortunately?) the plastic sleeve came with it so I was left with a hole about a foot deep. Searched for and bought a rotary washing line with the same diameter pole which came with a plastic sleeve which fitted in the hole to which the new pole fitted. Success.