Is there any sort of link between Bosworth Trail and Thornborough Road past here? there used to be changeset/27510797 , but that got deleted in changeset/27510797 .

A proper survey is needed to see what the access restrictions are (and to see whether it is a public bridleway or similar).

I'm sure that there's something here commemorating the Battle of Cropredy Bridge (the reason for the spur on relation/3165973#map=19/52.114783/-1.315245 ).
I'm surprised that it seems not to be mapped.

A car park with a capacity of -1 seems a bit odd?

What traffic is allowed to go between Colbeck Street and Shaw Street? An armchair mapper joined the roads, but the imagery suggests probably not. However, it's quite likely that foot or cycle traffic can get across - but needs a survey to check.