[link to original on tumblr]
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Both have a string of chords that all have a single common note, and they end in a modulation in which that single note falls a half-step (from a fourth to a third in relation to the root of the final two chords). In "I Know She Will," that common note is an A, which then falls to a G#. It's D major (D, F#, A), D7 (D, F#, A, C), A major (A, C#, E), Esus4 (E, A, B), E major (E, G#, B). In the bridge of "Care of Cell 44," it's a G note, which is further emphasized because it's the only note played by the bass until that half-step descent, when the bass goes back to the opening phrase. So, G major (G, B, D), A7 (A, C#, E, G), C minor (C, Eb, G), which - after going back to G major - repeats before going to Dsus4 (D, G, A), D major, (D, F#, A).
At first, I thought, "Oh, it's just Rod Argent doing the same sort of thing again," but then I looked up the writing credit for "I Know She Will" just to make sure, and I discovered that it's actually a Chris White song. I think I've always regarded Argent as the more sophisticated writer from a technical standpoint, but it seems that in the bridge of "Care of Cell 44" he was actually taking something from White's writing.