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I don't think people trying to access Fox Talbot Close via Epping Close is due to people using routing services based on OSM data, as he roads aren't connected in OSM.

That said, I've made a few tweaks, including changing Fox Talbot Close to a (private) residential street - it's not just a service road or driveway. I've also split it at the gate, so the stub between Baker Street and the gate is routeable. Adding vehicle=private to the gated portion wasn't necessary, as the access=* tag applies to all transport modes.
https://www.openstreetmap.org/changeset/164716098

It may take a few weeks for changes to propagate to routing software.