No, that shouldn't be their role. Unfortunately though the courts batted it back to the police, judging that the vigil wouldn't necessarily be illegal and leaving it up to the group to work with the police as to how it could safely take place. Clearly they couldn't come to any mutually agreeable way forward and it sounds as though there were threats of £10k fines for the organisers if it went ahead as an organised event.
I do appreciate the police were in a difficult position, but either agreeing to a socially distanced event with the marshalls being provided by the organisers (which the court ruling would have allowed them to do), or, when the non-official gathering happened anyway, taking a softer approach and not barging in and trying to drag away the speakers, would both have been better solutions. I don't think hindsight is needed to see that and whoever was in charge on the ground last night and thought taking that action would be a good thing needs to be hauled over the coals.
I do believe the term 'vigil' was a bit of a misnomer, as an element of protest was always part of the plan. Imo there were a lot of people there last night more interested in the protest than the vigil but that was always going to be the case from the moment the official event had to be called off. The police have to make judgement calls every day, I don't understand how they got this one so wrong.