I had a hedge of bay trees (Laurus nobilis). I cut it out, as it was puffing out too much and I decided to keep only a single plant (see picture to get the idea).
My point is that very often a lot of basal shoots come out from the old hedge roots and I have to cut them every time, unsuccessfully.
Can I have some hints about how to effectively prevent basal shoots from proliferating?
If you just cut down the unwanted plants and left the roots in situ, they will continue to try to grow all the time. The only way to stop that is to treat the stumps with stumpkiller, something like SBK brushwood killer (http://www.vitax.co.uk/home-garden/sbk-brushwood-killer/, by drilling into them and applying the product to the wells or holes you've made. If there aren't any visible stumps, you'll need to dig around and treat major roots in a similar way instead, obviously being careful that you don't treat the roots of the tree you want to keep by mistake. If you can't find SBK, there should be similar treatments available where you are, but if you do use SBK, although it tells you to dilute it, I never do for killing tree stumps, I simply apply the product neat, and very, very carefully, to the holes I've drilled, and cover afterwards. It's important not to spill it anywhere else, including the soil.
The other option is to remove all stumps and roots to a depth of a foot to 18 inches.
I don't think that basal shoots can be permanently removed. This plant tends to grow like a bush or multi stemmed tree. If you want to grow it like a standard (single stem) you will have to go against its natural tendencies. So regular pruning of the shoots whilst young and small would be the easiest, and probably the only option. Using stump killers would be fine as Bamboo has suggested on the rest of the hedge, if these are separate plants you wish to get removed.