On this occasion she was in 1st gear rolling slowly towards a roundabout, foot on clutch only, then applied the accelerater and the car surged ahead, and she needed to quickly apply the break, luckily this time no near misses...
If rolling towards a junction, why is a foot on the clutch? Take foot off and let the engine just pull gently.
If the clutch is fully down, then there is no drive. So this must mean you are either resting a foot on the pedal, bad practice, or holding the pedal slightly down.
Either of those may cause a little slip, but as more power is applied, the clutch may grab, taking full engine revs to the wheels, instead of losing some with the slip.
This may be a technique issue.
Find a local road with little or no traffic and good visibility ahead and behind. As flat as possible.
Move away in 1st gear, then let go of all pedals. Let the car just roll along with the engine on tickover.
Now gently apply the gas to increase speed. Pickup should be smooth and controllable.
Now change to 2nd, release all pedals and allow it to roll along on tickover again. This will demonstrate the lowest speed it will tolerate in 2nd gear. At or above this speed there is no need to depress the clutch.
Again, from there, gently adding gas should bring a smooth increase in speed.
Many cars will do this in 3rd as well, but will protest at the gentle acceleration.
When moving away, it is easy to be lazy and bring the clutch up before adding any gas. Sadly many instructors teach this way, as it is easier, so lazy. It is poor practice, confuses the engine management computer, and increases cylinder bore wear.
Should always add a little gas to raise the tickover before finding the clutch bite, then gas is added as the clutch is released. Only once moving can the engine be allowed to sit on tickover to pull the car along without gas.
Physics - Basic Inertia rules. It takes more energy to start something moving, than it does to keep it moving.
If the clutch is brought to bite without any gas, the engine computer is trying to maintain tickover against the added load. More fuel is put into the engine to prevent a stall.
As you then push the gas pedal, the first movement tells the computer that you will now decide on fuel input, but the computer is already feeding more than you are now requesting, until you've moved the pedal far enough. The computer responds by reducing the fuel input, which momentarily tries to cause a stall, so the computer adds fuel, discovers it is adding more than requested, and repeats the cycle. Some engines tolerate this better than others. Some will kangaroo, others just push harder than you wished. This is what may be happening.