IMO, your NAD M27 amplifier is amply capable of driving your KEF speakers. I am convinced that you wouldn't be able to hear a difference with any other good amplifier, even expensive Krell, Benchmark or Accuphase products, with the SPL at which you listen to your system.
You say that you're getting astonishing sound with your KEFs with the current amplification. You don't listen to music at insane high sound pressure levels. KEF speakers are designed to operate well with amplifiers with power ratings starting from 50 watts and up to 240 watts. They don't require 240 watts to be properly driven. No commercially sold loudspeaker does require that much power to perform adequately. For instance, pro audio speakers output more than 100 dB with only 1 watt input. The 240 watts rating actually is most likely the maximum wattage which they will stand for a peak SPL of one second or so, beyond which they will be damaged.
If you want to spend on improving your system, then look for speakers to replace your KEFs with better ones. In any system, the speakers are the weakest link. With electronics, you get diminishing returns rather fast with more spending.