The gates were locked opened when I walked down the path and there was a small sign stating footpath to Wilfred's lane from the Somerset place side. So I assumed the path is open to the public but now seeing that photo I'm wondering if my assumation was incorrect. 

I think some more research into the status of the path will be required. Unfortunately I won't be able to go and have a more detailed look as I'm no longer in Bath.  

I'll add the two gates on to the map