While you're learning the way described should be good enough but if you want the way recommended by the advanced driving community, it's a bit different. We try and avoid what's called "brake-gear overlap" or BGOL. The idea of avoiding this is that if you are braking and depressing the clutch at the same time you are in less control of the car and the weight of the engine is free to push the car forwards more, resulting in the brakes having to work harder.
We suggest this method (assuming a corner that be taken at around 20 mph from a 50 mph road):
1. Collect as much information as possible (where other drivers are, how tight the corner is, any hidden dangers)
2. Position the car towards the outside of the bend to allow you to see around the corner earlier but sacrifice road position for safety if needed.
3. While on the straight before the corner, brake down to the right speed for the corner.
4. Foot off brake onto clutch and select the right gear for the corner (probably 2nd). *you should still not have quite reached the bend*
5. Take your foot off the clutch and onto the accelerator. Turn into the bend and while on the bend apply a little bit of acceleration to keep the speed of the car constant.
Note about the last bit, you are maintaining speed, not increasing it. You should (in theory) have got the car at the right speed to go round the corner in a safe and stable manner.
Once you've exited the corner (the road starts to straighten out) speed back up to the safe limit under or at the legal limit.
This takes practice and is not the fastest way of cornering (although it does allow you to carry speed better) but it is the safest, according to the police drivers handbook and all of the advanced driving organisations. It's called "the System of car control" or just "The System" and one of the 4 "s"s - Safety, System, Stability, Speed (making good progress - not speeding) that you learn on advanced training, starting with Pass Plus. For the tech minded that's Information, Position, Speed, Gear, Acceleration.
Like I said at the start, if you're just learning, follow the advice of your instructors, once you've passed your test, then it's time to learn to drive properly.
HtH, MtMtMn