What's you're home power's stability like? If it's 0.3% or better, you just need a variac.
I was thinking 10mV resolution, Mains move more than 0.3% every second or two, so variac not even close to a solution.
I actually cobbled together an audio amplifier driving a step up transformer and I drive that with an HP signal generator and it’s infinitely better than a variac. I’m thinking of making more of an effort to come up with something more precise.
I wouldn't claim that it's a particularly stable source, but it's really not far off of your original specification. 0.3% of 250V is 750mV, a fair bit looser than 10mV steps, and with my 34461A's probes straight into a mains outlet at my bench, I've recorded +- 0.4V or so, which is just a smidge over your 0.3% specified tolerance.
What kind of current do you need? If it's very little, you could just cram a function generator through an audio transformer or similar and get to the right ballpark, but I'd be expecting 10s of uA on the output. May be easier to send the function generator through a BJT to get some current going, then step up the voltage by 50 or 100 in a transformer. Since the function generator is variable, it should give you pretty good tolerances as long as the output spec was better than 0.3% base accuracy and you calibrated out the transistor's, base resistor's, and transformer's losses in the system and had a good and stable supply for the transistor.