No. There isn't a correct way. The highway code specifies that a cyclist can take a roundabout like you describe or the way you would in a car.
I cannot advise strongly enough not to follow the "alternative" roundabout approach of riding round the outside with your arm pointing right until you leave. Just practise on roundabouts and get used to them, do them the same way you would a car.
Beware mini roundabouts, they are a lot more hazardous than they look, drivers rarely give way, will overtake, mount the island and even drive the wrong way round them. Once you master larger roundabouts you'll find it's the smaller mini ones that are the more dangerous, they can be pretty daunting at first.