I hold a PhD in political economy, and am outside academia; what route might I take towards researching for a PhD in canine psychology and behaviour? I hold a BA in a language and area studies (history, politics, social science) and a PhD in political economy (touching on social science), both from British universities belonging to the (research-strong) Russell Group, and I have been outside of academia for many years.

What route might I take towards the goal of researching for a PhD, preferably again at a Russell Group institution in Britain, in canine psychology and behaviour?

(I have read the help file, and felt that giving details of the fields was necessary in order to make clear what I am asking. Advice that is not specific to these fields is very welcome, especially if the size of the gap between them is similar to the size in my case.)
Given that you already have a Ph.D., can you network with anyone to meet a mentor in this subfield? Their personal advice could help you figure out which formalities you can skip and what skills are essential. Do they see your work as providing transferable skills to their field? Would they recommend that you need more background in lab work, psychological theory, or something else?

While it's not normally a good idea for people to try to contact unknown professors merely to ask for help preparing for a later application, you've been socialized into the norms of academia (especially within the Russell Group) and may be able to do so in a targeted and effective manner.