I too have an ancient Hotspur which occasionally has the same symptoms.
This actually happened an hour before I found the above posts.
The transformer needs a secure earth, or the high voltages will damage it. Make sure it's tightened down to the base of the boiler.
The usual problem I have is that, over time, the spark gap gets too wide, and the HT can't jump the gap easily, also it needs to be at the right height.
1) With the power definitely switched off, take off the front cover and manoeuvre the flame fail rod unit out to allow access to the chamber.
2) Ensure the spark electrode is slightly below the level of the heat spreaders, and the end is between about 1/4" (6mm) to 3/8" (8mm) maximum away from the striking plate. This will allow a good spark into the atomised oil, and keep the electrode a bit cooler, giving it a bit longer life.
3) Replace the flame fail rod unit, and refit the cover.
4) Note that the transformer needs a secure earth, or the high voltages will damage it. Make sure it's tightened down to the base of the boiler.
You can then switch on, and all should be well. You may get a slight oily smell for a short time, as the unburnt oil around the base of the ignition area will vaporise and result in a temporary smoky yellow flame.
After a few minutes, and around two or three runs, all should be well.
5) If whilst running, the flame is mostly yellow, there isn't enough air mixing, so carefully rotate the air intake vane at the bottom of the motor until the flame is mostly blue with some yellow. Don't adjust until it is all blue, or it will run too hot.