First off, you’ll probably want to grab a cheap digital tuner if you don’t have one (even a phone tuner is fine). That way you can make sure your harmonica is playing the notes you think: the harmonica’s reeds can go out of tune, which can make the harmonica play in tune with itself but not with other instruments.
You Will Never Work In Television Again definitely has a center pitch of C. Most of Thom’s chords feature a C as the lowest note, where it serves as a sort of pedal tone. There are plenty of scales with C as the root note, but in this case it seems to be the C-pentatonic scale. I don’t think I hear a B or an F during the entire song. So avoid those notes and it’ll probably blend a bit better.
That said, it’s always possible to add notes that aren’t in the main scale of a song. This is most obvious in minor keys, where modal mixture is frequently used to create the melodic minor scale. But in any key, you can usually find a “borrowed” note that sound good with a certain chord in a song, even if that note doesn’t sound good with any of the other chords. For example, an F will probably sound too dissonant during the first and third chords of You Will Never Work In Television Again. But an F will sound consonant with the song’s second chord, and it’ll add an interesting vibe since it suggests an alternate harmony (IV instead of VI). For a more dramatic sound, an Eb could also be played during the first chord (borrowing from C minor), though you’d need to approach that more carefully.
It’s also worth noting that both Thom the winds instruments are deliberately a bit sloppy about pitch. They often slide in and out of notes, instead of landing perfectly on pitch. In this case (and on many other Radiohead songs) it adds an element of uncertainty which makes things feel a little more tense.
Thom playing his mid-1960s Epiphone Casino in Royal Tan finish during You Will Never Work In Television Again during the Smile’s first broadcast at London’s The Magazine in January 2022.