Under most circumstances I would not go near a bridge that looks like this. We were near a pub that we knew was open and we had been walking through the wettest June week we could remember. Based on the idea that we couldn’t get much wetter anyway.
This bridge is on the Leicestershire Round, a 100 mile circular walk around part of the County. The path is overseen by the local council and is enthusiastically promoted by the Leicestershire Footpath Association. They also keep a valubale ‘updates’ page on their site about closures and diversions