To pull up on the right and park faced against the flow of traffic is not something I or any other road safety professional would recommend that you do. It does actually tell you in the Highway Code that you should avoid doing this. But for some reason the DVSA seem to want to encourage people to do this by including it as a test exercise. So here I will explain how to go about doing it as safely as possible.
What You Should Aim For

There are two elements to the exercise, the first is pulling up on the right in a safe place. Consider all the advice given for making a ‘normal stop’ and put that into practise. The additional problem here however, is that you may have to contend with oncoming traffic before crossing over. After checking to see what is behind you, choose your safe stopping place. If necessary, signal your intention to go to the right. If there is oncoming traffic, simply treat this as though you were turning into a side road; slow down, stop if necessary and wait for a safe gap before pulling over.
There is the potential for confusion here. If there are nearby driveways on the right for instance, it is possible that an approaching driver may think you are turning into one. They may stop to wave you across or flash their lights at you. Think! If there is enough room to pull over, then do so and acknowledge the other driver with a wave of thanks. But if there isn’t enough room, don’t drive across and block the other driver. Acknowledge their courtesy, but then point to the position where you want to stop in the hope that they then realise they are in your way. Hopefully they should drive on and leave you to it.
Observation
You will now need to reverse in a straight line for a couple of car lengths. This should be a very simple exercise though you do need to ensure that you take full and proper observation. Consider that you may be reversing across driveways, and any pedestrians nearby may possibly want to cross the road. So check over your right hand shoulder as well as to the front and rear before you set off.
The bulk of your observation should be over your left hand shoulder with regular checks to the front and right. If vehicles approach from the rear, you may be able to continue without affecting them; this depends on how wide the road is. However, anything coming from the front has to move out to go around you so you will almost certainly need to pause while they do this.
Having completed this short reverse you then need to prepare for moving off. Again, all round checks should be taken, finishing with a good look ahead and a blind-spot check over your left shoulder. This blind spot check is particularly important when moving off from the right as there is a large area your mirrors will not cover.
Things to Avoid
Do not make the mistake of thinking you cannot pull over because of oncoming traffic; and drive so far that you miss your opportunity to stop.
You are okay pulling up on the right if there is oncoming traffic which is a reasonable distance away. As long as you don’t take them by surprise or cause them to slow down or suddenly change direction to avoid you.
During the reverse, you should keep going as long as it is safe. If other drivers are about to pass you, do not continue to reverse if this will make it difficult for them in any way. Take your foot off the gas to pause for a moment or stop if you are in any doubt.
Control-wise, make sure that your car and wheels are parallel before you begin to reverse. If necessary, pull forward a little to straighten everything up. You should not then have to do any steering while in reverse. You should avoid allowing the car to drift away from the kerb and you should definitely not mount it!