The most common cause of hum is failing to connect the thin ground wire from the turntable to the preamp/amp -- you need it as well as the audio cables, which often have a floating ground for the cartridge +/-. 

If the hum is present in the headphones when the Phono input is selected but goes away when you select Tape or Aux, that confirms it.  However, if the hum is present in the headphones for all sources, then the NAD 3020e probably needs repair.  It is theoretically possible for the amplifier power supply transformer to induce hum into cables -- any cables, even plugged into & grounded to its own chassis -- and of course the phono is amplified much more than other inputs.  Still the missing phono ground wire is usually the culprit, even with old equipment.

Hi & welcome to Beoworld!
Have you thought about replacing the NAD with something like a Beocenter 2300 or 2500?. You’d have to put a RIAA pre-amp between the Rega and the Beocenter but this would work well & also give you the option of playing radio or CDs or even cassettes. Also the system could be remote controlled with a Beo4 or a Beolink 1000. If you take your time waiting for bargains on eBay this should be just about doable with your budget.

Cheers

Nigel

You’d also have to invest in some powerlink cables to connect the Beocenter to the Beolabs. Should still be doable with £250, especially if you go for a 2500 that has a defective cassette. There’s one on eBay currently for £180 including a Beo4.

One more thought.... if there’s no hum from the NAD with the turntable disconnected, it’s probably working fine. This could be sold for a few bob 🙂

Hi All

Thanks for all the responses. While searching for a suitable option, I liked this one :

Technolink TC-770LC

Ok .. So after much contemplation, I am thinking of getting a Graham Slee Gram Amp 2 Communicator as a preamp for the turntable. Specs are below : 

😁  Sorted.

I found an incredible deal on a Rotel RC-850 Stereo Control Amplifier (£30!!!) that looks and works like it is brand new. Connected it to the Beolabs using RCA cables (about 5 metre length) and the Rega TT.

Sweet as anything. All works exactly as I was expecting. All signs of hum etc. which I had earlier with the NAD are all gone - totally gone. Very nice sound. Thanks to everyone who helped.

I am also now thinking of connecting my Walkman Cassette player to the aux input on the Rotel ... that will bring back some memories no doubt!  😐