Which could mostly be achieved at a fraction of the cost by increased utilisation of tilt capable stock / routes .
Which schemes would allow Southampton to Leeds to be about 30 minutes faster (as you said mostly I'll not require the full 1 hour journey time saving)?
I would guess that it would require skipping station stops, if this is the case how do you serve those stations?
How do you provide capacity for the XC services (which are now traveling faster due to their tilt) to be able to get past slower services (which may not be able to benefit from tilt)?
The average speed would need to increase by about 1/3 between Birmingham and Leeds to achieve it all by speed increases.
Assuming the train distance is comparable to the road distance (120 miles) the current average speed is ~60mph, which then requires an average speed of 80mph. This would need to allow for the speeding up and slowing down at each station as well as the station dwell time.
I don't know about the existing line speeds, however I would guess that there's fairly little which is >100mph. As such, even allowing for tilt (which seems to gain about 15%) there's likely to be a need for sections to be upgraded.
Then consider that Reading to Cardiff on the GWML which is fairly flat and straight is currently ~1:35 over a distance of 110 miles with fewer stops and you can see why I'm asking the question.