> would it really make so much difference to run at 125mph and the journey take a little longer?
It's halving the time from Crewe to London from 100m to 50m, so that's a big plus. Every train going to Manchester, Liverpool, North Wales, North West England and Scotland will be an hour quicker - that's a 2 hour saving on a day trip.
> And would the project be cheaper if it didn't need to be so super-straight in order to be able to achieve the high speeds
No, the extra cost for high speed is negligable in the open country. If it's not straight it's using more land.
It's halving the time from Crewe to London from 100m to 50m, so that's a big plus. Every train going to Manchester, Liverpool, North Wales, North West England and Scotland will be an hour quicker - that's a 2 hour saving on a day trip.
> And would the project be cheaper if it didn't need to be so super-straight in order to be able to achieve the high speeds
No, the extra cost for high speed is negligable in the open country. If it's not straight it's using more land.