if you look at the quad website, quad ii/40’s run kt88’s and rating is 40 wpc (as mono blocks) ... whereas quad ii classic run kt66’s and are 15 wpc as a stereo amp, so here you see apples to apples the kt88 application has about 25% more power than kt66 (5 wpc more)
old school quad ii’s always ran kt66’s iirc (there are many refurbed old ones for sale, as can be seen via a simple google search), so it is evident in the new ii/40’s they uprated the internals to run more powerful kt88s to gain more output power
i think you could easily ping quad in the uk, or a usa quad dealer or quad importer, and ask if they advise users with ii/40’s it is ok to run kt66’s as a downgrade
rule of thumb i use is never ever run a power tube in a tube amp that was not designed for it... only bad things can happen (though some amps, like primaluna’s do have variable or auto-biasing that do allow a choice of output tubes... but this is usually not the case)
all this said, if they tell you that it won’t hurt anything to run kt66’s in the ii/40’s (other than having less power), then i suspect you will get a more ’tubey’ sound with the kt66 tube ... for the reasons i described in my earlier comments