The fact that the inductor has smoked indicates either:
Shorted turns in the inductor - you will need to replace it anyway if it’s badly burnt - so if it’s only a few turns of heavy gauge wire you can wind your own - just measure the gauge of the wire with a caliper, measure the core internal diameter (if it’s air cored) with a caliper, find a drill bit with the same diameter, slide it into the inductor and unwind the inductor counting the turns as you unwind. Count the number of turns in each layer if it’s multilayered. Buy some enamel copper wire of the same gauge and wind an exact replica of the coil. You can also buy wire enamel varnish to seal each layer but you need to wrap the drill bit in wax paper before you start winding or the coil will stick to the drill bit. I use drill bits as they pretty well cover most core sizes. If the inductor is wound on a ferrite former or plastic bobbin you just re-use those.
If it’s hundreds of turns of really fine wire then it’s a nightmare to wind.
If you know the value of the inductor from a parts list you may be able to buy one of the same value and wattage. But if you have an inductance meter you can just measure it - if it’s badly burned it may be open circuit - check it out of circuit for continuity first.
Or second scenario:
More likely a failed capacitor just after the inductor at the +2 feed point. If none of the resistors feeding the +3, 4K7 and +4, 100K are burnt then those caps at those points are possibly OK but the likelihood is they’ve all dried out and at least one if not all the HT caps are dodgy. If the first 50uF after the inductor fails it will draw heaps of current through the inductor - if they are all failing then their resistors will also get hot and so will the inductor.
I’d take all four caps out and check them.
If the grid of one or more of the EL84’s is shorting this can cause high current drain but the 330Ω resistor feeding the grid would be getting hot and burning also.
I’d check the +2 line point (power off) with a resistance meter with the tubes in and then with them out - if the cap is OK at that point you should get a high resistance reading, increasing as the cap charges up. If you have a low resistance reading and this goes high when you extract the tubes then whichever tube(s) is removed that causes that reading to go high is faulty. If the +3 cap is faulty the reading at the +2 point would be 4K7 plus the low resistance of the cap.
Best to check the capacitors out of circuit and check the circuit without them for shorts as well.
The chain of the HT power supply feeds is:
transformer>rectifier>+1 50uF cap>inductor>+2 50uF cap>
4K7Ω resistor >+3 50uF cap>100KΩ resistor>+4 50uF cap
All capacitors in the HT chain are 450V DC electrolytics, minus to ground.
You also need to check the rectifier and make sure none of the diodes in the bridge are shorted or open.