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I was told that since my new club had also paid the levy then this would be fine. I've no idea if this advice was technically correct
It is; as long as the club you're riding for has paid the levy, you can carry any sponsorship you like except a pattern registered with the UCI for a professional team.
Of course, the whole thing is a stupid legacy of the old amateur sport, and should be struck from the regulations as it serves no useful purpose.
My (uninformed) guess is that if you are racing for RCC then they will almost certainly have paid the levy so you should be OK on that front.
I spent a year racing in my uni skinsuit (which I think had sponsors on it) when I was no longer a member of the university CC... At the time I was told that since my new club had also paid the levy then this would be fine. I've no idea if this advice was technically correct though.