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Yes I think it would be important - without the access the service road is only a liability and there are other terraces that don’t have that issue. They don’t generally have off street parking though or rear access capable of taking building materials / plant.
Howard-
I don't really know what it means in practice, but on the Ealing map you linked to, the access alley (bit fancy calling it a 'road' :) ) is marked, in pink, as 'Adopted: Housing'. This mostly applies to estate roads, I think, but it may be a similar sort of deal here in that the local authority may also do maintenance on that bit. I think that may not change the land ownership, whoever's it is, but you could ask someone in Ealing's Highways department about it. This may all be bollocks but may be worth investigating briefly.
Oliver Schick
Worth a try, if the vehicular access to the rear garden is important to you. Indemnity insurance would also be a possibility - I suspect that ownership of the access road may well be something lost in the mists of time.