The designated UK square blue sign "cyclists dismount" does NOT have the same meaning as the OSM tag bicycle=dismount

The sign is only an advisory, which by itself effectively lets you know that you may continue riding. Historically used to show it was legal to ride, but the upcoming highway had an adverse condition that could not be improved. (low height, narrow, poor visibilty).
I repeat, it did not mean "must not ride." It advised you of an issue.

It also was allowed, confusingly, to be used where a cycle way ended, but a pedestrain way continued.  The intent to draw attention to an actual prohabition on cycling that is not clearly marked. (eg Pedestrian Zone).

The meaning has been updated. The original intent of advising of adverse conditions has been removed. It may only have been advise, but advising disabled people to walk breaks UK disability laws. The adverse conditions should now be signed to show the specific issue (eg Low Height (2m)). It is now only to be used together with other signs to confirm "No Cycling" exists at locations where it may not be apparent.

Now things get complex. In the situation your discussing. It is clear the intent is that the Cycle Track ends and you're not to ride over the foot bridge. But there appears no prohabition on cycling over that foot bridge.

Although we commonly say that "cycling on a pavement" is illegal in the UK. That is wrong. The prohabition is for vehicles, and objects with wheels, or animals, being taken onto a "footway" that is part of a road, but forms a lane in the road seperate from the carriegeway. (There is a legal difference between footway, footpath, and walk way). The bridge is seperate from the road, and therefore a footpath. Since it is a legislative Footpath and not a legislative Footway, there is no prohabition on non-motorised vehicles. A Traffic Order would be needed, and signed with a No Cycling sign at both ends of the bridge. 

In my experience the Highways Authority can't be bothered with creating a Traffic Order, and has chosen to acheive their aim by misleading with the advisory Cyclists Dismount sign. Putting up this advice sign does not require a Traffic Order with associated cost. 

There may be no prohabition of cycling over that bridge, but I would accept the intent of the sign and make the bridge bicycle=no.