In the hypothetical situation where the Railways Act 1992 doesn't get passed, you'd still have the EU directives to get through, and the incoming Labour government in 1997, which was all in favour of PFI deals. We have a rough idea of how they may have handled British Rail, because in our timeline, they had control of London Regional Transport (as TfL was then). They introduced the Public Private Partnership, or PPP, which was inherited by TfL but the process started by the government directly before TfL was set up.
Ownership of stations and track was passed to "Infraco JNP" and "Infraco SSL", sold to Tube Lines and Metronet respectively. Operation of the network itself remained with TfL, but the track stations - and uniquely the individual trains themselves - were owned by the Infracos. They swallowed billions of pounds and ended up getting taken in house, just as their mainline cousin Railtrack PLC had in 2002.
So we'd have definitely got some form of privatisation, and given they felt the need to break up the Underground network for competition purposes, you can infer they'd have done the same with BR. Possibly a Railtrack InterCity, a Railtrack NSE and a Railtrack Regional Railways? Each being sold on a 30 year PFI deal to a private consortium in return for crayonista improvements like moving block signalling, etc. They'd have gone bust and ended up getting taken in house.
I suspect on-rail competition would have been off the agenda, as it was heavily discouraged even under privatisation by the Labour Government in our time line as it was, as they saw competition as "wasteful" and abstractive of revenue. However, there was already pressure even in BR days for more competition with Stagecoach having made a foray into the ECML. With the requirements of separation under the EU directive, I would guess the most likely result would be the three business units becoming tendering organisations to private contractors. In other words, not far off what we have today, and not far off what Great British Railways will probably introduce.
Rolling stock could be owned by the infrastructure companies as on the London Underground. It would probably evolve into the ROSCO system we have. More Networkers and 158s rather than Electrostars. IEP is a government project, so something like that would have hapenned in a non-privatised timeline.
I'd think wages for drivers wouldn't be far off what we have now, because - as on LU - there'd have still been a Bob Crow and they'd have still been able to shut down the system, and the Labour government would have caved.
I don't think electrification or infrastructure improvements would have been as pronounced though. There'd be all sorts of promises made, but probably none come to fruition. Chiltern would be on the decline, and remaining services diverted to Paddington after which Marylebone would close. More government impetus to close expensive lines, single junctions, etc. Rather than the debate being "should we electrify Oxenholme to Windermere, and Wigan to Salford via Atherton", the debate would be "should we close Oxenholme to Windermere and put an 'Express High Quality Coach' and reroute Wigan to Salford via Chat Moss / Lostock or change it into a Parry People Mover run by the local authority"
I think fares would probably be the same as today, but with fewer special offers, advance tickets, etc. They'd probably have hived off rail networks in PTE areas to be self-contained and locally specified. That may have led to many of the PTE converting heavy rail to light rail or tram as many wanted to do anyway.
Yes, there would have been less profit going out to owning companies *. But that doesn't magically mean it all gets reinvested into the Railway. It just means the government doesn't have to spend as much subsidising the rail network, so they wouldn't. So taxpayer's money would have been saved.
(* in theory. Of course a lot of the profit that got leached from the railway came in under the Labour government with the 'Cap and Collar' franchise agreements, where the government messed up big time and got outwitted by the owning groups. Their record on PFI deals, including London Underground, Schools and the NHS leaves a lot to be desired, so it's quite easy to envisage that even if not privatised they'd have still messed it up and managed to lose billions anyway).