The new bike lane width might be slightly over the top BUT the idea is that there is room for fast cyclists to pass slower ones within the lane and allow cars to pass too.
Of course what the Daily Mail doesn't bother to show is what the road used to look like. For this we have to thank the marvel of Google Street View.
SO, previously the Council (as is common) thought it necessary to protect motorists from each other by separating them with a wide hatching zone. People on bicycles probably felt excluded, or scared.
In Edinburgh it would be nice if the vast expanse of hatching on the delightful Braid Hills Road was removed and a really wide cycle lane added. Of course to improve 'road safety' it might be necessary to reduce the speed limit too...