osrm-backend
                                
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                        foot profile routes on highway=construction
this is because profile.avoid does not include 'construction', and no tests cover this.
It may be intentional. For example in urban areas pedestrians are often allowed to use such roads to get to the destination i.e. shops or houses.
This issue, I think, is the one I'm encountering with Moneypenny Lane.
@maraf24 makes a good point which I hadn't considered. However, other algorithms (given the same data & origin + destination) do route around the lane (usually via Vauxhall Street then the footpath (way #938088198, way #938088199, way #173615145)).
In this case, the entire road (including sidewalk=*) is new. No traffic (except construction) is allowed to traverse it.
I presume access=no (or at least foot=no) should make the situation clear to OSRM? Recently set access=no in order to check the results, but I gather that'll take ~24 hours.
If so, the question then becomes one of how to handle cases where access-condition tags aren't explicitly set.
Having perused other issues in search of this one, a common response to complaints about routes avoiding any possible construction is that this is the safer option. However, a counterpoint for on-foot navigation is that a shorter route is much preferable.
Maybe these sorts of (ambiguous) situations need to have flags which can be toggled in order to influence the algorithm as a user preference for default behaviour for their locale?