May I ask your opinion on what is the best and most effective pattern for a VFR pilot to scan their instruments during manoeuvres?
A VFR pilot shouldn't really be "scanning" the instruments in the sense that an IFR pilot does; he should be scanning the sky for traffic (see my first answer) while using his peripheral vision to maintain attitude. Yes, he should periodically (and briefly) check the instruments to make sure nothing is amiss, but then go back to scanning for traffic. I wasn't taught any particular "scan" for that, just to look at whichever instruments seem most useful for what I'm doing at the moment.
If you're having trouble holding proper altitude and airspeed as a VFR student pilot (from a comment to other answer), you may be spending too much time looking at the instruments rather than not enough. That may seem counter-intuitive, but the key to both is attitude. Get the right attitude, using the artificial horizon or other instruments at first if necessary, then look outside at the real horizon (in particular, the relation of your nose to it) and then just maintain that picture while you do your traffic scan.
The only time a VFR pilot is supposed to be "scanning" the instruments is during hood training. For that, I was taught the "T" scan: assuming you have a six-pack in the standard arrangement, you focus on the AI (top center) and then briefly look left at airspeed, then back, then down at heading, then back, then right to altitude, then back. Repeat until the hood comes off.
(Answer based on original wording of question, which sounded like he was asking about scanning the sky for traffic.)
The method I was taught is to hold your eyes steady on each clock position for 1-3 seconds. This takes advantage of how your peripheral vision is more sensitive to movement. If your eyes are constantly moving, everything you see is moving, so your brain filters it all out.
For the same reason, if you know someone is there (CTAF or ATC calls) but don't see them right away, try looking 30° (one clock position) off angle either way to engage your peripheral vision.
Note that objects coming directly toward you don't move, which is why you need to scan with your detailed center vision to detect size changes. That also works better with the clock scan rather than continuous scan, but I'm not as sure why.