How do you do an uphill start without the handbrake?Watch
But you have to be very quick with it as you have to set the gas and lift the clutch just as the car starts rolling back.
OP: Your other alternative is getting on the bite just before stopping, or better yet avoiding stopping completely through proper observation (roundabouts tend to have relatively good visibility compared to other junctions). Other than that, you could use the handbrake in a quicker manor by simply keeping the button pressed throughout the whole thing which saves a bit of faffing around, always let it ratchet when you actually want to secure the car though.
That being said, it's only a minor. You should always look to improve, but I wouldn't make a particularly big fuss about it. Examiners aren't looking for a perfect drive.
I woudn't worry to much you're basically saying you dealt with it safely but were a bit slow getting going again after applying the handbrake - with time you'll become smoother and more efficient. The way you chose is ultimately the best method.