No, the true total 15/16 Government subsidy actually paid
to Northern Rail was £249.1m, equating to 10.7p per passenger-km or 17.3p per passenger-mile as shown in the DfT spreadsheet you linked. Northern used part of this subsidy to pay its £17.7m Fixed Track Access Charge to Network Rail, which Network Rail spent on operations and routine maintenance of the track, signalling and level crossings across the Northern network.
Additionally DfT paid the Network Grant of £4000m
direct to Network Rail for renewals and enhancements across the whole national network -see p3 of the
ORR Annual Statistical Release. ORR terms this grant Direct Rail Support, but DfT choses to call it an additional subsidy that it notionally divides between the TOCs in proportion to their Fixed Track Access Charges, although it is not money that passed across the books of Northern or any other TOC.
The DfT spreadsheet you linked shows that it apportioned £260.7m of the Network Grant to Northern, equating to a notional additional "subsidy" of 18.1p per passenger-mile, for a total of 35.3p.
The DfT spreadsheet does not include Merseyrail, but if part of the Network Grant were apportioned to Merseyrail according to the ratio of its Fixed Track Access Charge to Northern's, Merseyrail's share would be £33.1m. Merseyrail's total 15/16 passenger-km were 695.7m, i.e. 432.3m passenger-miles, so the notional additional subsidy would be 33.1*100/432.3=7.7p per passenger-mile. Adding this to the actual Merseyrail subsidy of 16.7p per passenger-mile gives a notional DfT "total subsidy" of 24.4p, in line with your rough calculation.
But neither the ORR nor Network Rail publish a breakdown of Network Grant expenditure by region, still less by TOC, so DfT's assumption that it is proportional to Fixed Track Access Charges is purely arbitrary. For example, a significant proportion of Network Grant funding is currently going towards projects that are of no benefit to either Northern or Merseyrail, such as GWML and EGIP electrification and London Bridge and Waterloo station upgrades. On the other hand, Merseyrail has recently benefited from the Wirral Loop renewals and Northern from the Northwest Triangle electrification. None of this spending bears any relation to Fixed Track Access Charges, and Government capital expenditure on enhancements and renewals is not normally termed a "subsidy" in other parts of the public sector, e.g. roads.
The published ORR subsidy per passenger-km figures I quoted are based on the real net cash payments to Merseyrail and Northern and so are the best available comparative data. Extensions to Merseyrail would likely yield a negative return on the investment.