As
@LTig said, you cannot just throw more watts at a speaker. That said, I suspect 120 wpc is OK.
The KEF specs say max level is 110 dB, which at 84 dB/W/m needs almost 400w. That's for peaks. Their amplifier rating of upto 180w is likely their "nominal power" not their "peak power".
To reproduce 92 dB SPL @ 3m with 3dB of headroom (good for popular music, not classical or accoustic) at 84 dB/W/m needs 113 watts. So you are likely just fine.
These calculators (I use
https://www.crownaudio.com/en-US/tools/calculators "amplifier power required") are to estimate what you should buy. As has been pointed out, you have it, so if what you hear is OK, then you're OK.
If you want to, you could get a UMIK-1 and learn to use REW to see what your actual distortion figure is. If I were to bet, I'd say the mid- and high- frequency is OK but you'll start to see bass distortion playing really loud out of bookshelf speakers. They might also be coupling to whatever surface you have them on. This would call for adding a sub or changing the stands/feet, not getting a new amp.
If I were to do anything, I'd get that measurement mic (UMIK) and objectively test what you have. I bet it will be OK. Make your purchase decisions on data, not opinions.