I can't think of an answer that fits the OP's definition of "...whilst also taking cars off the road".
People like to big up regeneration when trying to justify re-opening some ancient route, it's a nice "sell", it ticks the kinds of boxes that politicians want to be seen to be ticking. People may argue against "gentrification" but it's hard to argue against "regeneration" - it's a handy unquantifiable argument in favour of whatever you want to try to justify.
But (whilst some lines have certainly increased
overall travel) I don't remember seeing any suggestion that there has been a noticeable drop in cars on routes like the A7 from the Gala area towards Edinburgh. Whilst I'm sure you can point to isolated examples of people who no longer drive (or no longer use the car for every trip that they'd previously have made), I'd wager that the majority of train passengers are those who fall into the following brackets (using the Tweedbank line as an example*):
- Borders people who have taken up jobs in Edinburgh as a result of the train service
- Edinburgh workers who have bought/rented houses in the Borders because the train allows them to live somewhere with a garden/additional bedroom etc compared to the expensive property prices in the capital
- Leisure journeys (people visiting the Borders because it's now more accessible for a day out for people who don't have a car)
- People who'd previously have used the bus (a service which has reduced in frequency since the train service came along, in common with areas like Alloa - Stirling)
...whilst those are valid reasons for using the train, they aren't taking cars off the A7, they are just adding to the overall demand. Similarly, pinning the hopes of re-opening a route on the promise of building ten thousand houses may mean lots of people using trains who wouldn't have before, but car journeys also going up.
I'm sure that you could argue that the Tweedbank line has reduced the increase in future car journeys, but that's not the same as actually reducing the number of current car journeys.
So, to use a future example, I would imagine that the re-opening of the Ashington/Blyth line will encourage Geordies to consider living in Northumberland (since they may be able to commute into Newcastle in comparable journey times to being stuck on urban roads, benefitting from a bigger house due to lower prices outside of the city) or Ashington/Blyth residents to seek work on Tyneside - and will certainly have a big impact upon the frequent Arriva express buses in the area - but I doubt that we'll see the A19 downgraded to single carriageway because the train service has significantly reduced the numbers of cars on the road
(* - I'm using Tweedbank as there aren't a lot of purely "urban" projects outside of London, and I'm not familiar with the effects of the London projects on things like road traffic)