His tail looks pretty good, please keep it very, very clean and dry, and it would be a very good idea to put either an antibiotic ointment/creme on it, like Neosporin or "Triple Antibiotic Creme", or you can use raw, unfiltered/unpasteurized Honey or "Makuna" Honey (do not put regular honey on it, it has no antibiotic properties). I'd apply the antibiotic or the raw, unpasteurized Honey at least once or twice a day, just dab it on the end right on the wound and then rub a bit around the tail above the tip. This will help make sure that if there is anything infection left it won't spread up his tail.
If you see the blackness AT ALL spreading up the tail (basically if the black part gets larger), then please get him to an experience reptile vet immediately, as this is an indication that it is still infected, and the black tissue is dead tissue and it's spreading up his tail. If this occurs, which I don't think that it will if you keep putting the raw, unpasteurized Honey or the Antibiotic Creme on it, the sooner you get him to a vet, who will most likely amputate right above the dead tissue, thus eliminating the infection completely, the less trouble this situation will be, as if you see it spreading up his tail and you wait to take him, this can really become an ugly, complicated issue. Like I said, I don't think this will be a problem for him, it's looks pretty clean, but I'm just telling you this as an FYI, just in case the blackness (necrotic tissue) spreads at all upwards...
In the UK I believe the healthy green of choice for Dragons is Arugula (Rocket as you call it). Stay away from any types of Kale or Spinach, they are loaded with Oxalates that will bind to any Calcium he eats and this keeps him from absorbing any of the Calcium he eats in his food or as a powder supplement, and they then just urinate/poop it all out. This is how people/animals develop Calcium Oxalate Kidney Stones. So no Kale, no Spinach...healthy, appropriate greens from Bearded Dragons include Collard Greens, Mustard Greens, Turnip Greens, Dandelion Greens, Arugula (Rocket), Bok Choy or Pak Choy (I know you have this in the UK as it is used in Thai cooking), Endive, Escarole, and Swiss Chard.