Can anyone confirm whether the single line ever was bi-directional? Having looked into it a bit more, I'm not convinced that there ever was provision for Up trains to run over the single line, but rather that rationalisation was simply a case of removing the Up line and connections at either end. If that's the case, I'd certainly agree that any existing redundant locking will be of little use for reinstating a single line!
No, it didn't go through being a bi-directional single line. The Up line was just taken out of use. I think this may have been down to the condition of some of the S&C but it was so long ago I cannot remember for sure, it could equally have been the condition of the plain line through the section.
I think it was 'billed' as a temporary disconnection, full recoveries of the locking weren't done at the time, the points were secured and signals disconnected. I don't know whether the locking/wiring etc. has ever been formally recovered, but as you say that would be of little use for making the remaining line bi-directional, as the signalling is double line AB, so one half of each instrument was probably just covered up and its wiring disconnected.
I cannot be sure, but a faint bell is ringing about a subsequent proposal to implement token block working to make bi-di, but that would have required PW alterations at Frodsham Junction to get onto the right road coming from Halton. I would guess that the facing crossover at Halton has been plain-lined by now, too. Whatever the cause, if there ever was such a proposal, I'm fairly sure it's pretty much dead and buried by now.
I hear the Liverpool - Halton section is currently in the early planning stages for resignalling to get rid of the mechanical boxes, so it's unlikely that there'd be any inclination to carry out expensive alterations to the existing system.
