AC mains LED flicker
well aquainted with electronics. I'm not!

each fed from 240v ac

 smoothing capacitor across the dc drive

No, not at the level of detail appropriate to this question.

These LED light strips run from 240 V AC line power.  That's not something you should be messing with.  Getting this wrong can cause electrocution to you or anyone else that might touch these lights, burn down your house, possibly violate your electrical code, and almost certainly invalidate your insurance if these modified devices are found to have caused a problem.

We can't tell exactly how the conversion from AC to the DC the LEDs run on is accomplished.  Deep inside there may be a point where hanging a capacitor on would smooth out ripple.  Without a schematic, that's hard to tell.

Basically, you bought the wrong lights.