I haven't, and from your thread you've done plenty of digging in other council areas so well done! Street-level imagery shows what may be byelaw signage at the point this path meets the Great West Road, which might shed some light - but I no longer live in London so can't check. I suppose I was taking a different approach of mapping only affirmative signage, as the cycleway to the south and another on the east side of Lampton School are signed as shared cycleways, while this is not, and the omission leads me to mark this as foot designated only. Perhaps the most pragmatic option is to add a fixme tag asking someone to survey the path and check smallprint signage at North end to confirm whether bicycles are allowed?