Let us say that this does come to pass, and frankly I doubt that it will (rain dampens things no end - you'll see), here are the numbers to work with:
Total regular, territorial and reserve strength of the army comes to a rounded 265,000. From this one must subtract the 10,000 ish in Afghanistan. Figures for deployments other than in Northern Ireland are somewhat inexact, so let's say that there are 250,000 soldiers available. To this can be added 8,400 Marines. Trying to tease out figures from the RAF and the Royal Navy is just too difficult, so I will not be attempting it.
The Met's numbers come to 37,484 - sworn officers plus specials. Obviously it is not worth including PCSOs.
Greater London has a population of 7.7 million. That GL and the Met area are not coterminous does not help, so I will pretend that they are one and the same. That 7.7m equates to a rounded 13% of the population. So, assuming that Shropshire, Cumbria and the Shetlands etc are as entitled to protection as London, London should get 13% of the available manpower - a rounded 33,500.
That combined Police/Armed forces figure comes to a rounded 71,000 - a rather thin red line of one citizen in uniform per every 108 civilians. Clearly the looting classes are largely comprised of a particular age demographic - let's say 15-30, and are overwhelmingly male. That population comes to a shade under 800,000. Which changes the ratio to 1 to 11.
Now if the populace, and in particular shopkeepers, were as well armed and as supported by the law as they are in, say, Texas, this would never have gone so far, would it?