Here is a summary of comparative ranks.

It looks to my untrained eye as if a Commodore is a lower half of a rear admiral, it sounds very uncomfortable.
http://www.helsinki.fi/~degroot/anglomil.html

Googling tip for non-experts, like me: I tend to throw lots of words at the search engine (leave out the inverted commas). "Commodore" just gave me a load of old Commodore 64s, "Commodore UK" didn't fare much better. "Commodore Navy British" did a little better. Fishing around with "Commodore Compare ranks" gives some other options, eg http://www.toshiro.f2s.com/oob/site/data/india/ranks.html which gives ranks in India. So if your first attempt is too general you can fiddle around with the entry information to refine your search, without having to get too technical.