I saw the above in the Guardian today and was astonished. I quickly found this, but for the previous year, in Scotland, where the rate seems to have been significantly higher, 13 times higher:
I appreciate the limits of comparing crime figures between a country and a mega-city. The rate of rape conviction in Scotland had dropped from 49% in 2015/16 but was slightly higher than it had been in 2008/09, when it had been 37%. One-year statistical variations are not generally considered to be reliable indicators of a trend. You need at least 5.
I could not easily find recent conviction rates for other parts of the UK but did find this for 2007 when the Scottish rate had been around 37%.
Note that the conviction rate in London in 2007 was 14% compared to 3% today! Then from the USA:
These seem like stunning differences in the quality of policing and in the attitudes of those working across the justice system to the experience of victims of rape. In Scotland, rape has the lowest conviction rate of all crimes, so I’m not suggesting that 39% is necessarily satisfactory. I don’t know enough to have a strong opinion.