Well, UNIT was/is a United Nations organization, not a British one …
Also, one of the conceits about Torchwood was (seems to have been dropped in season 2) that it was so ultra-top-super-duper-hush-hush-secret that nobody was supposed to know about it. Which, if you think about it, makes it bloody hard for an organization to operate. So, you could envisage a situation, back in about 1970, something like this:
The Brigadier: Right. I’ll sort out the security clearances. Good to have the Doctor on board.
Torchwood operative: (crashes into the Brigadier’s office, strikes impressive pose in war surplus overcoat) Not so fast, Lethbridge Stewart! You cannot employ the Doctor! We forbid it!
The Brigadier: Err … yes … quite. And who are you, exactly?
Torchwood operative: (strikes impressive pose in war surplus overcoat) WE … are … Torchwood!
The Brigadier: Jolly good. And what are you doing in my office without proper authorization?
Torchwood operative: (strikes impressive pose in war surplus overcoat) We have all the authorization we need! WE … are … Torchwood!
The Brigadier: (surreptitiously presses button marked “Call Sergeant Benton to get loony out of office”) That must be very nice for you. But what authorization do you have, exactly?
Torchwood operative: (strikes impressive pose in war surplus overcoat) You’re not cleared to know that.
The Brigadier: I mean, are you Home Office? Ministry of Defence? Foreign Office?
Torchwood operative: (strikes impressive pose in war surplus overcoat) WE … are … Torchwood! We’re ABOVE the Government! BEYOND the law!
The Brigadier: Well, quite. That must be jolly nice for you, and I’m sure we’ll take everything you say very, very seriously. Now, why don’t you go off with Sergeant Benton, there, and he’ll make you a nice cup of tea? (The extra-calming kind, please, Benton. If you catch my drift.)
Torchwood operative: (strikes impressive pose in war surplus overcoat) Don’t forget, Lethbridge Stewart! You are to have nothing to do with the Doctor! We forbid it … and WE … are … Torchwood!
The Brigadier: Jolly good. *(Watches Sergeant Benton escort the Torchwood operative out of the office.) * Strange man. Oh, well, never mind. (Carries on filling out the Doctor’s security clearance.)