Rotol was a joint venture set up by Bristol Aircraft and Rolls Royce (hence Rotol; RO from Rolls Royce and TOL from Bristol) to manufacture constant speed propellers, as De Havillands were unlikely to be able to produce "their" CS unit in large enough numbers. I say "their" CS prop because it was it was in fact a license built version of the Hamilton Standard CS propeller. The Rotol propeller went on to become the "standard" prop only on Spitfires from the MkIX, I believe, but on earlier marks, both DH and Rotol props were used.
The MkVc Spitfires that fought the Darwin campaign in 1943 all had the DH prop, and it gave a lot of trouble with overspeeding. The standard tactic was to get above the inbound Japanese, who had learned from the 1942 campaign to approach at 28,000ft, which was about the limit of the escorting Zeros. So the Spifires climbed to 30,000ft at which height the oil in the CS unit congealed. Investigation in Australia showed that the bleed back ports between the front and rear chambers of the CS mechanism were too small, and when the plane was nosed over into a dive, the propeller was likely to act as a fixed pitch unit, resulting in an over-speed.
Some of the MkV's used in the defense of Malta were also equipped with the DH prop. The Rotol prop was used for the most part, but was slower revving than the DH unit, and Spitfires equipped with the DH prop had an extra 500rpm to develop more power to get off the smaller British carriers used later in 1942 to re-equip the Malta garrison. The Rotol unit was OK for getting Spitfires off the larger US carriers used earlier, but when the USS Wasp was lost, the British had to use their smaller carriers. This is something those of us who change props on the A2A model can appreciate
. I believe that most early Seafires were equipped with the DH unit, because of the need top get off Britain's smaller carriers, but as they didn't generally fight at the same altitudes as the RAAF at Darwin, the inherent design fault of the DH manufactures unit wasn't an issue.
Please note that I don't claim that the above is in any way definitive. The more I read on the subject, the more I realise that there is more to be researched. Morgan and Shacklady's book is very good, but should be read along with others. Wartime operational necessities in all the campaigns that the Spitfire took part in meant that the standard Spitfire, of any mark, is not the Spitfire that might have been used in the field.
Cheers,
Mike