This is one reason why I've always shied away from Rega as a brand, another being most of their amplifiers look pretty ugly imho. I have a Denon pma 800ne in silver, looks terrific, sounds sublime and no hum whatsoever (maybe this is due to the iron core transformer) and I got a ridiculously low price for a nearly new one. I recommend it to everybody who asks about good budget amplifiers.
Transformer hum is not unusual and is normally a mains problem, sometimes related to other things connected to it ie. appliances etc. Some products are better of copying with it but transformer type, size, quality also plays a part. Rega use perfectly fine transformers and I would guess, perfectly adequate in-product mains filtering. These days all products have to comply with standards. Rega employ capable electronics engineers.
Rega is no different to others. I believe you also had an issue with an Audiolab 6000A for a similar reason (?) whereas I had absolutely none in either my old or present place.
One possible solution is to try a good DC blocker. It may be throwing money at a problem that could/likely lie elsewhere but it works for some and if you order from somewhere which is accepting returns you should come out on top.
You could also try and tighten or slightly loosen the transformer fixing bolt, some add isolation rings, unplugging appliances, chargers etc one by one to see if there are culprits.
Last option is to have your supply tested for accuracy. A guy over at PFM did that and the result was his supply was too high and was an actual fire hazzard.
Having said all that, exchanging the unit first if you can makes sense. It could be faulty. Perhaps take it to another place and plug it in briefly to see/hear whether there is transformer buzzing too. If not, it's your mains.
I feel for you as must be annoying. One of these things which, once heard can't be unheard. I only had a transformer hum once with a NAD Receiver some 30 or so years ago (frame transformer I believe). Changed it 3 times at RS but never solved the issue. Hope you have better luck.