In the USA the highest rank a Boy Scout can achieve is Eagle Scout. What is the highest rank possible for British Scouts?

Queen's Scout is the top level for British scouts. Not just boys, but girls also as we are mixed. One of my fellow Cub Scout Leaders (and a Venture Scout still until our District gets the new thing called Network going), Tilly, has just achieved this. She will be presented with her award at Windsor later this year. Network is the replacement for Ventures, for 18-25 year olds.

I assume you are asking about the highest AWARD achievable in UK. Rank would refer to Leadership structure. In the UK we removed all 'rank' markings many years ago, and now all wear the same type of identifying badges, from the Chief Scout to Beaver Scout Leader.
Baloo was quite right, however, in stating that the Queens Scout Award is the highest achievement. But we also have Explorer Belts and other awards for high achievers. Hope this answers your question ?