Is there any merit in this approach i.e. double regulation to produce a more stable output or should I just use a single regulator?
I'm guessing the theory is that you'll end up with effectively doubling the PSRR (Ripple Rejection). I guess if you start with a lot of noise, reduce it by 72dB (typical PSRR of a 78xx), and then reduce the resulting noise by another 72dB you'd be ahead... but how much noise are you really needing to reject? Even if you started with 1V of ripple, 72dB of rejection would knock that down to 250uV. Add 40uV of output noise, and you're around 300uV. Is that low enough? Depends on your application. Running it through a second regulator might reduce it even further, but that seems excessive.
If it isn't good enough, think you'd be much farther ahead to use an already-regulated (preferably linear) supply with low ripple and then just run it through a single regulator with good quality input and output filters. Reducing the ripple to 0.1V should get you down to 25uV+40uV. Much lower, you're going to have to find a better regulator. For instance, use a LDO with much better noise and PSRR ratings such as a LT3042 (just the first one I found). It looks like across most of the spectrum it's 10dB better than the 78xx which means you knock that 0.1V ripple down to 8uV, and even better, the noise voltage is only 0.8uV, so you're down to <10uV.
Personally, I'm skeptical that you need that low of noise on the rail. More importantly, it's going to take very careful design to both achieve this, and also keep the rail that clean. 10uV is nothing. To put this into perspective, if you have current ripple on the rail of even 1 mA, and you have a rail resistance of even 0.01 ohms, you're going to induce 10uV of voltage ripple just because of voltage drop.
I'd start backwards at this point - start with how much ripple can you tolerate and then build your power supply system accordingly. One note here is to not underestimate the utility of local power supply filtering - an appropriate ferrite in the right spot can do wonders. In the few spots where I've really cared about noise on the rail for a part, I've used that approach instead of trying to filter the rail itself to some unobtainable low value.