Funny, I was just editing the photo below from your garden when I got the message with your posting, Katerina. The Carpobrutus edulis certainly looked good there, I hope you will be able to tame it.
I planted some of the pink ones many years ago to cover some naked ground, they definitely did the job. Now I am getting plenty of exercise pulling them out again, but they are very good at improving the soil, and they are wonderful for the compost heap; the weight is perfect for clamping down the dry stuff, and they are adding moisture. I also have a yellow one, which is much better behaved, it does not seem to spread much at all, much less that your specimen, in fact.
I am envious of your big Echium candicans just behind the Carpobrutus.