For that kind of headset, at this stage normally the fork would come out.
So I would try:
First try some proper penetrating oil, and leave it overnight. If you can't get hold of that easily something like WD40 might work better than ordinary oil.
Then borrow a large hammer. For this job I would use a mason's hammer or a large claw hammer, a sledgehammer is too big.
Support the bicycle so that the front wheel is a few cms off the ground (or get someone to hold it like that).
Get a thick piece of wood to protect the end of the steerer tube.
Whack the piece of wood really hard with a large hammer.
But perhaps first wait to see if someone else has a less brutal proposal.
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When reassembling, use some kind of antiseize grease. I reckon ordinary grease is much better than nothing if you don't have the proper stuff.
I think Thorn use something like Copperslip, it is sort of rust coloured. I have a small pot of silvery stuff that I have had for many years.
I use this on seatposts, stems, steerer tubes, eccentric, etc.
It has worked for me even when neglecting Thorn's advice to do an annual dissassembly of seatpost/headset - on one bike I left the headset for 5 years without any problems.
