I never worked for BEA but I did work for Dan-Air as a Licensed Radio Engineer and have seen more variants of Comet than most.
Decca and Doppler are two distinct navigation systems and not the same thing at all. Decca is/was a hyperbolic navigation system relying on ground stations, a Master and three slaves. Doppler is/was a self contained system with no external requirements.
The ex BEA 4bs were fitted with Decca as, in Dan-Air service thay had blanks where the Decometers and the moving map display were fitted. They did not have Doppler. In Dan-Air service they were conventional Dual VOR/ILS, Dual NDB aircraft with no other aids.
The Comet 4s did not have Doppler or Decca and were conventional Dual VOR/ILS, Dual NDB and Loran aircraft.
Some 4Cs were equipped like the 4s but with the addition of a dual Doppler system. Not all were so equipped.
I have never seen any Comet other than the BEA 4bs with Decca.
HTH.