The cheapest option is probably going to be build your own transformer. Warning: its *NOT* easy and you may not be able to source magnet wire for the secondary within your budget unless you can sweet talk a local electric motor or alternator rewind shop to let you buy a part spool at trade prices.
Suitable 'donor' cores and pre-wound primaries can be found in microwave ovens. If you don't have any high voltage experience start by reading the SAFETY section of
https://www.repairfaq.org/sam/micfaq.htm so you don't kill yourself if you encounter a HV capacitor that hasn't fully discharged.
Scavenge the mains transformer from a dead microwave (not a high end inverter model). Ideally choose a 800W upwards microwave, as you need 400VA and that should give plenty of core aperture area for your new winding. A 700W microwave probably has a big enough transformer. A 600W one probably isn't going to work well - although it can handle the VA required, the restricted area will make it much more difficult to wind, and as microwave transformers are not intended for continuous operation, you need to over-rate it if you are going to re-purpose it for continuous use.
It needs to be a line frequency transformer, that's in physically good condition with no signs of serious overheating or burning. Secondary to core or secondary to secondary insulation failures are acceptable as you are going to be cutting away the old secondary. Primary to core, or primary to secondary insulation failures are *NOT* acceptable. A quick test with a Megger or other high voltage insulation tester will save you a lot of time and effort if the transformer is defective.
Carefully cut away the high voltage secondary and filament supply secondary, taking great care not to abrade or otherwise damage the primary. Knock out the remains of the secondaries from the core apertures, knock out the magnetic shunts, and check there is no damage to the primary.
At this point you should power it up and check that it doesn't draw an excessive no load current or heat up excessively before you invest more time effort and materials. If it looks like its OK, leave it on for several hours and monitor the temperature as Microwave primaries often have barely enough turns to keep out of hard saturation as copper is expensive and the extra losses are acceptable if the duty cycle is limited and/or it can rely on extra forced air cooling from the microwave's fan. Worst case: you may have to use an extra 'buck' transformer
* to feed it, dropping the mains voltage 10% or so, but if it overheats you'd really be better trying a different model of microwave transformer rather than adding an extra transformer.
Now add a 10 turn temporary secondary using hookup wire so you can measure the volts/turn so you can calculate how many turns you need to cram in there for your application and from the aperture area, what's the maximum wire gauge you can use, allowing enough margin for the wires not packing perfectly and to make it possible to thread the winding in there and to be able to add 10% more turns to correct the loaded output voltage. N.B. that will give you the NO LOAD volts/turn - you can expect about 10% less fully loaded.
Get suitable wire, and prepare the core by taping the edges of the apertures so you don't scuff the wire insulation on the sharp corners. This is also a good time to add extra insulation between the primary and your new secondary if the primary doesn't already have reinforced insulation. If you've got Kapton tape, great, use it, but worst case you can do a good job with cartridge paper and ordinary clear varnish, if you fully saturate the paper with varnish,build it up in enough layers, squeezing out excess varnish and hold it in place with waxed paper and sponge rubber to keep the pressure on till the varnish has fully cured. Don't use PVC electrical tape for transformer insulation - it melts too easily and the adhesive turns into slippery goo when hot.
You then have the really tedious task of threading the wire through the core apertures to lay down the new winding so it helps to have assistance to handle the loop as you pull the wire through for each turn. You are going to be handling a *LONG* loop of wire that its critical not to kink.
Start by calculating the length and allow 1/3 extra - running short is a disaster and you may need to add more turns when you load test it. If you need two identical windings, (or a center tap), double the wire over and start from the middle treating it as if it was a single wire, but taking care not to twist them as you lay down the turns. Take the end and tape it in place to the face of the core in line with the center leg - make sure you've got enough spare end length to terminate it properly. Coil up the end and secure with tape so it doesn't get caught on anything as you wind. Lay down an even winding one layer at a time. It may help to tie the wire down with cotton thread at the end of a layer before starting the next. *DONT* lose count of the number of turns.
When you've got the calculated number of turns on the core, temporarily secure the free end, (*DON'T* cut it), and strip the tip of the inside end you previously coiled up and taped out of the way, and the tip of the excess wire of the outside end.
You can now power up the transformer again and check the no load current hasn't increased (which would mean a shorted turn), check the no load secondary voltage, then load it to your max design current and check the load voltage so you can calculate how many turns to add or remove to trim it to the voltage you need.
Its then just a matter of adding or removing the final turns and making a good job of securing the outer winding end, and terminating the windings. If you need a center tap, cut the folded end to separate the windings and connect the inner end of one wire to the outer end of the other. Magnet wire ends should be protected by thin sleeving slipped over them which must be properly secured to the winding and/or core *after* the outer winding end has been secured so it cant unwind at all.
* The buck transformer secondary only has to carry the microwave transformer primary current, which will be about 1.7A for 400VA at 240V so it only needs a 2A rating. Even for a 9% drop you only need a 50VA 24V transformer. If you only need to drop 5%, a 25VA 12V transformer will do the job. Wire it as an autotransformer with the secondary in series with the primary, initially phased so the secondary voltage adds to the primary. Move the Line input connection to the free end of the secondary and take the reduced line voltage output from the old Line input terminal. If the secondary is center-tapped you can alternatively take the output from the secondary center tap for half the drop. 
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