Firstly, looters, and burglars in general, deserve to be shot. They are nothing but vermin.
Secondly, we had a right from time immemorial to keep and bear arms in our own self-preservation and defence. All free people have this right. It has been illegitimately taken from us by successive governments in the 20th Century. This is due to the return to dominance of ideologies based on state power. Whether of the supposed left or the supposed right, they all reject individual liberty and uphold collectivism in one form or another. The left version couches its state worship in the language of democracy. i.e., the state = the people. The right justifies its position by telling us we need to respect authority. In the past this authority would have been ordained by God himself, but this last part is usually lacking now, so tradition can be substituted for divine ordination.
Such left versus right distinctions are superficial in reality. They merely explain the constant battle between each faction for control of the state apparatus. Neither side doubts for a moment the legitimacy or need of the apparatus itself. They both see it as imperative in order to keep down those who dissent. The right harks back to the Ancien Regime of Throne and Altar, to the 'good old days' when everyone knew their place. All the left - by which I mean socialist, communist, social democrat or whatever nuanced name it goes under - ever wanted to do was install its own leaders into the positions of power, in the hope that they'd share out the plunder from the defeated old guard.
There is no great physical struggle between these two factions any longer. They have fused together into a unified political Establishment. They are two wings of the same bird of prey.
The libertarian position is outside of this, because it is based on individual liberty, not a doctrine of state power. The only legitimacy the state can accrue to itself is as the defender of this individual liberty. It can claim no powers to itself, which the individual does not possess. Neither God nor the majority provide an excuse for crime. To a libertarian, the policeman's power derives from the individual's power to defend himself and his property from aggression. It may be delegated, but it is not alienated. Thus, the state has exceeded its authority egregiously by enacting legislation preventing individuals from defending themselves. By disarming the public, the state has become the aider and abettor of every violent criminal who aggresses against another individual.
Thirdly, there is no need for new laws and new prohibitions. Every crime committed during the rioting is amply covered by the law. That does not mean that the criminal justice system is functioning well, far from it, but the problems long pre-date the riots, and they relate to the sentencing, not the statute.
The failure of the justice system to treat serious crimes seriously has been given new exposure, but it is not news. The press have paraded countless examples of preposterous judgements from judges, following guidelines from the political class, which show a complete disregard for their traditional function. Cossetted by their wealth, perhaps, addled by the prevailing fabian doctrine, they go through the motions like a priest who has lost his faith. Casting down their eyes from the ivory tower, their blurry vision cannot distinguish between victim and aggressor.
If there is to be reform, let it be limited to the punishment. We need no new crimes.