No. It clearly states that the brown area is the householder's access area, but adds a caveat that threatens access being denied if the householder fails to contribute a proportion of the upkeep.
It doesn't matter whether the adjacent neighbour's garage has, up to now, hindered access or not.
The deeds speak of the future, and should Pusb's house become owned by someone with a Pontiac, the neighbour's garage might well be a hindrance, as it may be now, or shortly become so, when Pusb wishes to get his Mini on the public roads.
The developers of the houses, envisaged, and ensured in the issued deeds, that house holders would have reasonable access to the rear of their gardens. I don't think that they contemplated a light aircraft getting down the lane and into a garden, but by 1936, motor cars were becoming commonplace, and by providing the triangular portion cut off the gardens, they accepted that something less maneuverable than a bicycle or wheel barrow would need to negotiate the corners, and made provision for this in perpetuity, in the deeds to Pusb's property.