First up, the big ticket item that dwarfs all other investment is Crossrail, which London is partly funding from direct (local) taxation. If the tax money is removed then that is going to significantly alter the money that is "fair" to spend elsewhere in the UK.
Taking the £16 billion that the UK government is likely to spend on Crossrail 2 (the remaining 50% is likely to be funded by London) and splitting it between the number of rail passengers in the London and South East region (where the vast majority of the benefit would be seen) and you can then work out the funding per passenger to work out what investment should be placed in other regions to result in a per passenger investment figure.
As Crossrail 2 is focused on increasing existing capacity (an increase of 10% of rail capacity in London) rather than reopening or new lines, which is the reason for choosing a per passenger figure (rather than a per population figure) as in much of the UK there area areas where the population is spread in such a way that rail isn't a suitable option which still holds significant numbers of people.
Investment in Rail by region (based on DfT Crossrail 2 budget and distributed on a per rail passenger basis)
Region
East £2,348,000,000*
North West £1,736,000,000
Scotland £1,295,000,000
West Midlands £1,110,000,000
Yorkshire & Humberside £940,000,000
South West £669,000,000 (fixing Dawlish anyone?)
East Midlands £441,000,000
Wales £413,000,000
North East £213,000,000
*The Eastern Region is likely to also benefit from Crossrail 2 whilst other areas in the South East won't, as such there is likely to be some reduction in this figure to be spent in parts of the South East which wouldn't benefit from Crossrail 2.
In the Guarden news story linked to it lists three projects for the North West, North East and Yorkshire & Humberside totalling £1.6 billion based on the above figures would mean that during the construction of Crossrail 2 there would be a need for nearly double that funding (£2.9 billion). However based on just the DfT budget (i.e. excluding London payments) for Crossrail then the above projects probably are broadly a similar budget figure (although that does exclude other investment that is benefiting London).
I would suggest that if the per person spend (rather than per passenger spend) was used for a prolonged period of time then there could be a lot of empty new lines in a lot of the country outside London and the South East as projects are pushed forward just so the investment spend is maintained.
That's not to say that other regions don't need more investment, rather investment may not be as big as some (including the links above) are suggesting that it needs to be to be comparable to London based on a per passenger level of investment.
Yes there could be suppressed demand in the other regions, however any new line/reopening to serve new markets should be evaluated on case by case basis.
