it wouldn't affect polarity in so much as the ring simply failing to work if you take an open circuit to mean both live conductors are disconnected, so no circuit would lead to no current flow (with no alternative path fault condition aswell) so the protective device if wired properly would not operate ie cut out.
There will be no effect on polarity. I've tried very hard to see how it might trip an RCD but it looks highly improbable. I assume you have only one break. As Breezer says, you now have two radials, well almost. The neutral return is still a ring and so is the earth. When you plug something into this hybrid radial/ring circuit current flows out along one cable only but returns through both. This will cause unusually large magnetic fields around both cables because of the unbalanced currents. The RCD will still see the total current and should not trip. I don't really think that unbalanced capacitive coupling will be significant.
You are unlikely to notice many effects. The voltages at your sockets will be a bit low and, if you load one 'radial' up to the full 30 (or 32) amps, the cable will get rather warm. If you know where the break is fix it.
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