The Police don't seem interested and this reliance on CCTV is laughable. The authorities rely on CCTV so they don't have to attend when something happens. The simple truth is they don't have the manpower to attend everything as it happens.
It's not that the police aren't generally "interested" in crime - it's more that we're fighting a relentless battle with one hand tied behind our collective back.
Sorry as I am to hear of another street robbery (which, incidentally, I can't think of a single colleague that wouldn't like to solve such a case), on the facts presented, there simply isn't enough to make any significant headway in the investigation. The legal standard of proof we have to reach to prove a criminal case is very, very high - many would say impossibly so in a great many cases. The legal system massively favours the defendant throughout.
Casting my eye loosely over the very brief facts, you have this scenario:
1) No witnesses that can recognise the suspects' faces. This is, of course, because they were all wearing hoodies. Even if you saw the same three lads next week wearing exactly the same clothing, the defence will argue that clothing does not constitute identification, because it is easily portable and changeable.
2) There is no forensic evidence. This is because there was minimal contact between the suspects and victim.
3) There is no CCTV evidence. As the OP said, there are no cameras in the area.
4) The property stolen is impossible to trace. Cash is the most easily explained away of all stolen property.
5) The injury sustained by the suspect will not make him identifiable. Even if the suspect were stopped around the corner, assuming he had the nous to ditch his top - something a great many criminals do very quickly - clutching his nuts, he would explain it away as a cycling injury / football hit him or some other such nonsense lie. We would have to prove otherwise.
Even if the police were to receive an intel tip off (which happens more often than you might think - criminals are often very quick to squeal on each other) and the purse were recovered, with the passage of time the CPS will still not run a charge of Robbery. They would run, at best, with Handling Stolen Goods - assuming that you could positively identify the purse, and not just as a similar type. If not, the matter would be dropped. Even if "word gets around" about who is responsible, it will only constitute hearsay; it will simply be denied by anyone accused of the robbery.
Sadly, I fear that the best that might happen is that the police might eventually get to know what happened and who is behind it, but it seems very doubtful that a prosecution could follow with so little evidence left behind. Believe me, I hate criminals with a manic passion - but the system is very, very much against us. Even with a conviction, the sentence that follows is usually meaningless. This week, for example, I have charged another youth with yet another theft of a motor vehicle (aggravated, because he crashed it through someone's garden wall). Already, by the age of 15, he has racked up three convictions for residential burglary, and around 6 for various motor vehicle thefts. He also has a handful of minor drug and shoplifting convictions. In all, he has been arrested about 40 times, of which about 20-odd have resulted in a conviction. He has never done any time inside, or even come close to a Young Offenders' Institution. He won't end up serving any for this, either. I appreciate it's not Robbery, but even then the only time I have seen a youth end up with a spell in the YOI for that is on a second or third conviction.
If the general public could see the average criminal's PNC Record (criminal history), you would be shocked at how many times most of them have been arrested and convicted. You would also find that almost all of them have, at some point, received a "community order" of some sort; most are permanently under one kind of order or another. It would also make you see just how ineffective such "punishments" really are.
I will save observations on our general lack of manpower for another thread. I am, however, sorry that yet another innocent person has become a victim of crime.