Governments have been saying they'll level up or boost regional growth or whatever forever. It is actually a very hard thing to do.
Most countries of our size can only boast one "major global" city which is where finance, business, culture is concentrated. Cities grow around knowledge based economies and companies will flock to the same city (or small number of cities) for their industry because it is then easier to attract the right staff, poach someone elses employees, buy smaller rival firms and merge them etc.
The UK is only big enough to support one global level mega city - so the south will always be lifted by its proximity to London. Same as the regions around Paris in France or Milan in Italy (note it's not necessarily connected to government, Milan is a bigger, wealthier and more expensive city than Rome)
Better rail links could lift specific towns in the Midlands or North by making it faster for people to get to London but it won't be that widespread an effect.
Improving public transport from deprived regions to their nearest city of any size would be best for lifting local deprivation. If people can easily access more diverse work and education opportunities in Newcastle, Leeds, Manchester, Birmingham, Cardiff etc then that would go a long way to pulling particularly deprived places up. Public transport from the Valleys to Cardiff or from parts of the NE to Newcastle is poor - if it was good, reliable, fast and affordable, it would do more to level up the Valleys towards Cardiff than almost anything else. But it won't make them as expensive as London and commutable reach of it.