The figures didn't match what they were saying not long ago, and once again they were using the meaningless "numbers injured". Like the term "seriously injured", it's basis is too vague to be of any use.
The one absolute is number killed in London. They were comparing 2006 with now, and that tells a very different story. In 2006 the total killed was 19, average for that period. Currently the average is down to 13, varying between 10 and 16 in the most recent years.
So it's fatal accidents down by 32%, with their claim of a 16% increase in cycling over the same period. Even that 16% increase figure is suspect and probably larger in truth, the London Bike Hire Scheme (Boris Bikes) was introduced during that period and I'd think that alone added hugely to the total amount of cycling.
So just as elsewhere in the world, more cycling leads to safer cycling.