It's straightforward with only a little bit of maths. The classic equation for LM317 output voltage is:
Vout = 1.25v*(1 + R2/R1) +Iadj*(R2)
- where, in Naim's implementation R1 = 220R and R2 = (3k3 + 680) since the two are connected in series. So, ignoring the Iadj value since the current down the adj. pin is fairly small, you need to alter the values to get the multiplier (1+R2/R1) up to about 24.
The easiest way would be to put a new resistor in parallel with the 220R resistor to drag its composite value down to 170ohm. This means about 790ohm, or use the nearest, larger preferred value (810R). Better still, fit a 1K multi-turn trim pot connected as a variable resistor across the 220R and you will be able to trim the output as fine as you like. Just start with the pot set for max. resistance and wind it down from there, metering the output voltage as it increases.