Arthur Wallace is an agent with MI37.
He will be, soon enough. It will actually happen a bit before that he learns of the existence of MI37. MI5 and MI6, them he had known of all his adult life; pretty much every adult in the U.K. has for decades. MI37, on the other hand, nope! Not a clue. And that is pretty much how the government and the Director of MI37, Felicity Shaw, wants it. If the majority of the people in the country knew of the organization, they would inquire as to why it existed. And when they learned the truth there, well, it would not be good to have an entire populace unable to sleep at night.
And besides, publicity would not do MI37 any good. As Shaw tells Wallace, "We certainly don't advertise our existence the way MI5 and 6 do, but that just means the politics of intimidation are not useful in our arena. It doesn't mean we're not real". As to why this intimidation is ineffective, it is because MI37 operatives are not spies nor do they go hunting other spies. MI37 is "sworn defender of Britain's sovereign borders from threats thaumaturgical, supernatural, extraterrestrial, and generally bats**t weird".
Need examples? How about tentacled horrors from another dimension. Or a zombie T-Rex? Or Russian cyborg wizards. Or space alien spores. Or a demi-god going through puberty. Yep, crazy don't begin to cover it.
Wallace is not an agent when we meet up in the first recorded adventure. He is a detective with the Oxford Police Department, a man who puts his age as just a bit into the second half of his 30s. He is in okay shape, in his opinion, unless there are a lot of stairs to climb, then not so much. He likes his job because he likes solving mysteries and catching bad guys. He does not like his job when those bad guys start trying to kill him. He tells us over and over that he is most definitely no hero.
He also tells us, and shows us repeatedly, that he bases his decisions and actions on a very simple question: What Would Kurt Russell Do? A huge, gigantic, perpetual fan of Russell and every movie he has ever been in, Wallace ponders that WWKRD query every time something serious pops up and since they pop up a lot, he asks it a lot. Much to his regret, though, because, "God, that question gets me in so much bloody trouble".
Helping Wallace out once he is pulled unceremoniously into MI37 is his co-working, Kayla, about whom he says, "her superpowers are only outnumbered by her psychoses". Interesting woman is Kayla.