Fritz Wright, aka the Vengeance Man, is an agent of the British Government.
That is about as close to a definitive hierarchy as I can figure out. When the series begins he is a loyal member of the British Army's elite SAS and has been one for quite a few years. He has seen action in various well known hotspots in the Middle East and knows the lay of the land good enough to know he would rather not be there anymore.
However, really good operatives often get seconded to other organizations and when someone with the ability to fight like a berserker and often with as much control is needed, it is often in the best interest of the sister agencies to look outside their ranks, just in case something goes south. Wright is the man they started to call on and he is the first to tell you, things always go south.
When the Cousins asked MI6 for a bit of help, they called on the SAS and Wright was pulled in. The job was, as the British say, a right cock-up from the beginning and Wright's handling of some aspects of it were less than orthodox. So, when the southerly turning point was reached, it was Wright who caught the short straw. He thought he did rather well, all things considered. Apparently no one else thought that, however.
So officially he is in the dog house and unofficially he is just the man that other people could make good use of, especially if there is no direct link between him and them. So Wright stays busy enough.
But not so busy that he cannot and does not find time for some extracurricular activity. He finds, without looking hard in the least, people who have been dealt a very nasty blow by people who are too well connected to have anything to worry about. He finds that upsetting. They invariably find that Fritz Wright being upset at them is not a good thing.
Unfortunately for Wright he is very careful and very good and very human and it comes to the attention of the authorities that a vigilante is at work and some smart people put the clues together and realize Wright is, well, the right man. They could stop him and they do try. They could also see ways of using him even more.
The Vengeance Man is sometimes a very busy individual.