[trigger warning]
In previous posts (one, two, three) I tried to quantify how many falsely-accused suspects would actually be helped by the reporting restrictions.
Because it's so rare for a false accusation to lead to a trial, before which press reporting naming a suspect is extremely rare, the upper bound is probably around one person every three years, and the actual figure may well be significantly lower.
In exchange for this, how many does it directly harm by reducing the methods available to the police to gather information or identify a suspect.
Reporting restrictions between arrest and charge probably won't cause a problem in practice. Suspects can only be detained for 24 hours (36 with senior authorisation) without charge, which means that by the time the press deadlines come round, they'll probably either have been charged or released. If charged, the restrictions no longer apply. If released, the press are unlikely to report anything for fear of contempt of court and/or libel cases.
Before arrest, however, there might be more of a problem. I searched Nexis for cases in the past 12 months where an e-fit had been released and reported in the press or other media (among other similar anonymity-removing detection methods). I found 9 distinct cases, some reported multiple times. In at least one of these cases a conviction was secured.
Allowing for the possibility of cases where a description was reported but not an e-fit (and so the search didn't find the report), and where the suspect has not yet been caught and convicted but will be in future, this seems to give 1 a year as a reasonable lower bound on the number of rapists caught and convicted through these methods, with the actual number likely to be higher.
If only between 10% and 15% of rape victims make a report, and only around 4% of rapes are reported, this means that the average convicted rapist is likely to have committed many more rapes or other serious sexual offences before being caught. Weinrott and Sayler (1991) suggests that the mean number of rapes committed is around 10 times the number charged for, and some of the previous studies they reference suggest a higher value.
This is not surprising - the combination of low reporting rate (for which there are very good reasons, by the way) and the high attrition rate (for which many of the reasons are not good) means that the justice system selects for the most prolific serial rapists in its convictions. (And then sometimes gives them lenient sentences and lets them go to commit more crimes, but that's a topic for another time).
So, we can probably assume that by successfully imprisoning a particular serial rapist, we not only get justice for their previous victims, but also prevent numerous other victims of rape, other sexual assaults, and other non-sexual crimes (consistent with Lisak and Miller, Weinrott and Sayler found that these convicted rapists had also committed numerous non-sexual crimes).
So, if the coalition's proposals prevent the use and press reporting of e-fits, the proposals as a whole will protect one victim of false accusations every three years at best, and allow at best tens of additional crimes.
In other words, in the absolute best-case scenario, for every person this proposal helps, hundreds of people will be harmed1. Anyone voting for it or supporting it must be held fully accountable for that harm.
Postscript
If the proposed law ends up worded such that it avoids this problem and allows the police and press to continue co-operating as they do on distributing information about wanted criminals, then it is vanishingly unlikely to directly do anything at all.
Indirectly it will still contribute to rape myths and rape culture (though the effect of this will be harder to quantify) and should still be opposed even in that case.
1 Since some of these harms will be relatively minor non-sexual offences, and some of them will be rapes, it's probably not even worth trying to determine how severe the harm prevented versus harm allowed is beyond the number of victimisations.
