Aside from the ~£30b raised in fuel taxes, there's also the ~£6b raised in vehicle excise taxes.
Both of those revenue streams go into a government general fund and are not allocated specifically for road maintenance, because they collect about 3x what is actually spent on highway & road infrastructure each year. [1]
In short, the roads & highways are massively profitable.
London's buses however, lose nearly ~£1b a year, which tanks the entire public transportation budget, and more than offsets the profit generated by the Underground.
TfL actually received ~£3b in subsidies in 2018. That's compared to total gross income from the LU of £2,799m.
> The total of resource and capital grants receivable by TfL in 2018/19 amounted to £3,016m (2017/18 £2,477m). [1]
Total expenditure on roads of £539m, minus Congestion charges of £230m, means that subsidies received by TfL (covered by fuel duty & VED revenues) exceeded TfL road maintenance costs by £2,707m.
The LU does not subsidize the roads. It's actually the other way around. The net-subsidy (a.k.a government's net loss) on the LU is calculated at 9.7p per person-km, compared to a net-taxation (a.k.a government's net income) of 3.8p per person-km for driving.
"London has about 1/6th of the UK's population, so let's assume 5bn/year comes from London" isn't a good assumption - very few people drive/own cars in London.
The central government does not pass on this income to Transport for London (TfL). So TfL has to fund the maintenance of the major roads (aka Red Routes) in London from the income from London Underground.
Taxes on fuel used in motor vehicles (duties and VAT) are something like 30bn GBP/year in the UK.
London has about 1/6th of the UK's population, so let's assume 5bn/year comes from London.
That's 5x the annual operating profit of London Underground[0].
Government income and expenditure is fungible, so it's hard to determine precisely whether X is paid for by Y or by Z.
But it's clear that government revenue from London road users is much higher than the profit from London Underground.
So it seems strange to assert that roads are paid for mostly by London Underground.
[0] https://news.ycombinator.com/item?id=20865111