Working for an agency, how are my rights affected...

So I've learned about something called "AWR" (Agency Workers Regulations). Where after 12 weeks of work through an agency you are entitled to additional rights.

What I'm unsure of is if my 12 week period will start again if I switch jobs through the agency... So technically I am still working for the same agency and the same client, my role has just changed as if I have had a promotion. Nothing altered as far as my details go (same email, holiday hours weren't reset etc.) only a wage increase as the job went from being an agent in one office to a team leader in another, nor did I have any gap between switching roles.

Im based in the UK