I don't think it's really fair to say that one system that wasn't fitted would "almost certainly" have saved lives as compared to another system that wasn't fitted.
If ATP had been fitted and been operational on the affected lines and trains at Ladbroke Grove and Southall, these trains would not have passed signals at red, and there would not have been railway disasters at these two locations. Also, how effective would TPWS have been even if it had been fitted at the time? During the hearings into both of these accidents, I read every single word of the transcripts, and this was discussed. But as it was a long time ago, I forget the details.
Lord Hidden in his investigation into the Clapham Junction Railway Accident says under recommendation 46: "The Court welcomes BR's commitment to introduce Automatic Train Protection on a large percentage of its network, but is concerned at the timetable proposed". My I remind you that said report was provided to the Secretary of State for Transport on 27th September 1989.
Meanwhile 34 years later, at the current time, Network Rail is still having difficulties getting the funding for ERTMS. Technology keeps moving on. With the railways (actually the government) still dragging its heals and kicking the can even further down the line.
At some point, there will be an accident that could have been prevented by ATP or ERTMS if fitted, but not by TPWS. Even when introduced, TPWS was described as a "stop-gap" solution. And as it happens, it was not as cheap to fit as originally thought.
Now, I don't have the time to go through and analyse every single railway accident and incident to provide a list of the outcomes if ATP / TPWS was fitted.
For those that are of the view that TPWS alone caused the number of signals passed at red/danger to fall need to do better research. TPWS was one of a number of other changes that were introduced.
But at the end of the day, at the vast majority of signals, if the driver makes a mistake (human error), beyond AWS, there is nothing to override the train controls and bring the train to a safe stop.
To all train drivers, please do not take offence, as it is not my intention to undermine you. By far, the vast majority are excellent and very professional. But having talked to drivers, listened to the voice recording of drivers conversations with the signallers or read drivers written reports after incidents, it is clear that occasionally human errors occur.
NB. The communications/reports referred to above are in relation to allegations made against the signalling system, not accidents. All such reports are fully investigated internally by the railway. Sometimes, it is an equipment malfunction. Sometimes it is human error (driver, signaller or occasionally some other member of staff). Sometimes, it's actually none of these, and it's an oversight in the system or a design problem.