The word "freecall" seems to be only used in the UK and, if the controller tells you to "freecall", that's when you will need to pass your details all over again.
Outside the UK you will need to do this if told "squawk VFR/7000 and contact/try <...> on <....>".
The US also has an automated/electronic handoff system that reduces radio babble and manual telephone calls between controllers.
Once you have been handed off just say callsign, current altitude, and target/cleared altitude if climbing or descending when checking-in.
Because it was VFR I had to remain outside controlled airspace
Actually you only remain outside when you DON'T have a clearance.