At the height of the Ori invasion, their ground troops were spreading through worlds more quickly than anyone had planned, and whilst their ships were easier to avoid and worlds could be evacuated before they arrived, battalions began marching through the gates from captured worlds.

The US went to a state of full ground war, committing hundreds of soldiers where necessary.
However, even the US couldn't uphold such commitment on its own, as well as conflicts on Earth.
They turned to the nations who they knew would help.
The UK, Australia and Canada.
These commonwealth powers, along with several smaller European forces, provided funds, materials and troops to the SGC.
Already possessing a small on site Garrison at the SGC, the UK enlarges this to a special taskforce of 500 men with more in support.

After the defeat of the Ori, the UK and US have a severe falling out over the treatment of UK personnel. The UK pulls out of SGC operations and pulls funding.
In order to assuage the UK, a garrison is allowed on Atlantis, under the same conditions of the unit in Cheyenne mountain. 50 men with scientist back-up. Answerable to the highest rank present, no matter nationality etc, but with operational autonomy to explore the Pegasus galaxy.
However, expected to help fund and defend Atlantis at all times.
After a few months, the UKGTF returns to the SGC, assisting in all aspects of the program

Also, the IOA has funded its own SF unit, made up of specialists from the US and other nations. After secretly building an F303-hybrid ship of their own, their units go out in the galaxy collecting intel and gauging threats the SGC might not reveal of their own accord.

Here starts SGA - Allies. But who is really on who's side?

Message in a Bottle

Transmission

"...that we have reconed and assessed the situation, situation is critical and will need support, for we have already gathered this information a week ago, since we took the long way to Atlantis... (secret IOA ship built up from a 303 since its smaller than a 304) we have not engaged any hostiles yet, and we have not been able to contact Altantis...(transmission breakup)... we are 1 light-year away from Atlantis and we have been taking a cloaked jumper to other...(transmission breakup)... known stargates in the nearby systems...(transmission breakup)... again situation is critical and will need back-up. my team of 5 men and 25 black-ops and a crew of 50 maning this stealth ship with limited weapons (5 Mk VIII nukes, 4 railgun mounts, and 1 Asgard Beam cannon) and we only have 1 ship bay for 2 302s and 1 jumper...(transmission breakup)...we have seen a large build up of unknown ships, NOT WRAITH...looks like...(transmission breakup)...Renegade-...(transmission breakup)...and again we have very limited weapons...(transmission breakup)...we have a surplus of small arms fitted for the crew and my teams...(transmission breakup)...today at 2055 hours...(transmission breakup)...my jumper came in contact with a "scout ship"...(transmission breakup)...it ...(transmission breakup)...see us but it looks like it has similar technology towards the...(transmission breakup)...advise that we pack more nukes and firepower...(transmission breakup)...there seems to be a shield and an organ-...(transmission breakup)...we can only assume that the standard Mk VIII...(transmission breakup)...to disable it or destroy it...(transmission breakup)...no idea on smaller fighters...(transmission breakup)...it is safe to assume that our small arms will do the trick...(transmission breakup)...we've took photo recon-...(transmission breakup)...found a scouting party on a surface of a planet...(transmission breakup)... and it looks like they are wearing...(transmission breakup)...which it seems our 6.8mm and anything above that can...(transmission breakup)...for sure...(transmission breakup)...

...again requesting support, cordinates will be transmitted as soon as you reach 90% of the journey to this galaxy around the...(transmission breakup)...quadrant...(transmission breakup)...we will maintain our position until reinforcements arrive...(transmission breakup)... we'll be waiting for you...(transmission breakup)...

-wilco Major, out"

Weir didn't know about the IOA ship, and in her ignorance sent a team to the nearest planet to the transmission, in order to find out what is happening.
Apparently, whilst the 303-Hybrid Nightcrawler was making its sweeps, they ran into Wraith trouble on a world the Wraith were thought to have abandoned.

Major Macara, having served with Trang in Afghanistan, heads a rescue team that Sheppard tries to stop, as there is no proof that it is nothing more than an elaborate Wraith plot. Major Macara knows better, and thus ignores Sheppard's athority (remembering that officially, he has to do nothing that the USAF say, because, well, he ain't US) and proceeds through the gate, his own men forcing Atlantis staff out of the gateroom in order to use it. He won't leave a comrade in trouble, or a ship full of service personnel in enemy hands...

From here, the main story begins...