The problem I had was that I wanted to use the forks that came with a vintage frame I bought with the modern handlebars I already had. So I fitted the forks using the correct threaded headset with no issue, but modern handlebars and stems fit a different way to the old threaded forks. In basic terms the steerer on old threaded forks is much shorter than modern forks - on modern forks the handlebar stem bolts to the top bit of the forks (known as the steerer).
How to fit a threadless stem and handlebars to threaded forks.
First of all you'll need to buy a quill stem adapter like the one shown in the photo below:
Slide the adapter into the top of the threaded forks and use the hex bolt on the top to fix the adapter into the 'steerer' of the forks.
When you measure the adapter diameter compared to the internal diameter of your handlebar stem you might notice there's a bit of a gap (see below). Apparently this is normal.
ID (internal diameter) of my stem
OD (outside diameter) of the top of the quill stem adapter
You can buy shims to bridge to the gap, and to be honest I reckon that's probably the best way forward, but if I didn't finish this bike build today I wouldn't be able to cycle to work tomorrow, so I made a shim by carefully cutting open an empty beer can. The inside of the can appeared to be coated so I roughed it up by rubbing in on the old stone steps by my back door.
Pull the shim around the quill stem adapter nice and tight, and then use a tiny bit of tape to hold it in place while you slide the stem fixing over it. I really like how this beer can shim looks, it's almost a shame it won't be on display!
All done! Some folk think modern stems look terrible where they are replacing an old quill stem, but I think this looks just fine. Please do make sure you get everything set nice and tight, a loose set of handlebars can be very dangerous for obvious reasons!