There was a huge difference in staff fatalities between the 1970s and the early 1990s before privatisation, in particular a lot changed in the 1980s.
The early 80s saw the introductions of high viz vests., by the late '80s end of things like working in tunnels with trains running through, had occured along with heavy restrictions in working after dark in what are now red zones and the introduction of PICOWs (now COSS). Also the 1980s saw the end of most goods traffic and yard shunting of unfitted stock (by far the most risky environment). Spotlights on the front of trains also appeared in the last years of BR (try being lookout in the middle of the night with only an oil lamp or 2 figure headcode illuminated at the front of the train!) By the time of privatisation staff fatalities were I would suggest little higher than they are now.
Since privatisation the big changes have been:
1) Rimimi
2) Introduction of large numbers of contract/agency workers and much more mobility whereas under BR people stayed in a particular area.
3) Mandatory hard hats and covered head to foot in orange overalls (eg shorts banned)
4) Massive amounts of paperwork to prove that things are safe.
5) Train delay charges
1) Rimini has undoubtably lowered staff incidents, however from a very low base and at a high financial cost as evey last thing has to be planned and documented in advance, ending the days when a gang could be instructed to go onto the track, work out a safe system of work on the spot and do the job. It could be argued that if the government abolished this and put the subsidy into eg the NHS more lives would be saved, but that is a far wider philosophical question.
2) Introduction of large numbers of contract/agency workers and much more mobility whereas under BR people stayed in a particular area and worked under senior staff who knew their patch as well as a driver knows his route. I don't think anyone here is likely to argue that it has made things safer. It has undoutably made Rimini essential.
3) Mandatory hard hat wearing (anywhere rather than at "building site zones") and staff covered head to foot in orange overalls (eg shorts banned). This has no doubt saved some minor to moderate injuries, however a hard hat is very uncomfortable in hot or very cold weather and heavy overalls as opposed to shorts are very uncomfortable in hot weather. If someone is uncomfortable they don't concentrate properly and are therefore more at risk on the track. I'm not convinced the balance of risks is correct with this one, especially as it seems to me to be as much about image as protection.
4) Massive amounts of paperwork to prove that things are safe. This is partly due to (2), partly due to there now being many contract interfaces rather than command structure and in big part due to numerous EU health and safety regulations such as the Construction Design and Management regulations aimed mainly at the poor record of the construction industry but also applicable to the rail industry. This means that something that was left to an engineers professional judgement now has to be proved exhaustively with all sorts of tests and reports which is expensive. There is also a danger of people thinking lots of paper = safe. This largely is a result of outside regulations that coincided with privatisation and would have happened under BR if privatisation had not occured. The allowing of lawyers to advertise and conditional fee arrangements under the Major government also made all companies and their insurers VERY risk averse even on trivial matters (as does the need for companies to be insured by commercial insurers - BR self insured)
5) Train delay charges mean an incident in which, say a power cable is accidentally cut with minor or no injuries becomes a far more serious matter due to train delay charges (whereas before it was just an annoyed area manager and a dressing down for someone after a "Dear Bill" letter from the regional manager to the regional head of engineering discipline). The problem is that although real money these are pass the parcel payments within the industry, but the money to fund procedures to avoid them comes from extra government subsidy.
In summary. BR were well on top of the problem by the early 1990s, and staff injuries were by then so low that measures to reduce them further were disproportionately expensive (cost to reduce staff incidents like anything else follows an exponential curve that means the closer to zero you get the more the cost of every reduction). Additionally outside regulation and the increased mobility and use of contract labour associated with privatisation made more restrictive safety measures such as Rimini essential.
It is very simplistic and frankly childish to claim BR were useless and things now are a new nirvana, the issue is far more complex than that.
Personally I think it would be a lot better, now that newspaper trains are a thing of the past, night freight is on a few routes only and sleeper trains very rare to do most work on most lines in Engineering Hours with the power off every night (on 4 track routes a different pair of tracks every night) as a certain other still nationalised railway already does, which gets rid of the need for things to be booked three months in advance with a three month wait if it goes wrong on the day. Wouldn't work on all lines but I suspect it would on a lot.
Edit
Figures for fatalities struck by train due to failure of safe system of work 1990-2009
2009/10 to 2013/14 (all staff fatalities on NR)
It is clear the big change was in the early 1990s
before privatisation, since when figures have been more or less constant at 0-4 a year.
Source 1990 - 2009: Annex 1 of this document:
http://www.deathbyhealthandsafety.co.uk/platformx/resources/1010DRKTWSv1.pdf
Source 2009/10 onwards:
http://www.networkrail.co.uk/aspx/4815.aspx
