I’m asking of the six bands identified by Wiki.
I’m also asking for answers off the top of your head- no googling.
I would have guessed three I believe (two are obvious).
Ok, my WAG right off the top of my head -
the Beatles (obvious)
the Rolling Stones (obvious)
Eric Burdon & the Animals
the Zombies
the Yardbirds
Herman’s Hermits
The Kinks & the Moody Blues didn’t hit it big in the states til the end of the invasion, I think.
With a special mention for Petula Clarke who was the first (and perhaps only?) female artists associated with the British Invasion.
Beatles
Rolling Stones
Dave Clark Five
Herman’s Hermits
Gerry & the Pacemakers
The Animals
Great answer but a few weren’t correct. I would add that I am sourcing one Wiki entry (obviously I won’t say on whom) so we could have a few debates on this.
BTW the correct answer wins nothing. If I can remember the correct answer tomorrow.
My post above was for Don Draper.
JJ Zipper- again for close but not spot on. I was going to bed- almost midnight. Now I feel obligated to stay up 
The Beatles
Rolling Stones
The Animals
The Troggs
Small Faces
The Who
Those were the six that I thought of before I looked at the other answers. Confident in the first three, 50:50 about the fourth, and the fifth and sixth are just filler.
Gosh, I am surprised (and happy) about the quick responses.
**
Jessmagic** you are half right. You guess which half.
I’d say Beatles, Stones, Who, Kinks… and I’m not sure after that.
Skammer, you got a lot right but you need to count to six (sorry, this thread has turned into fun fior me)
Beatles
Stones
Kinks
Dave Clark Five
Gerry and The Pacemakers
Chad and Jeremy
Getting very close. I’ll have to stay up to answer this even though my wife is giving me the evil eye for opening another beer.
Without reading thread:
Beatles
Stones
Who
Kinks
uh
Animals
Herman’s Hermits
After reading thread: delete Herman’s Hermits, add Yardbirds.
Beatles
Stones
Herman’s Hermits
The Animals
Dave Clark Five
Manfred Mann?
I love telling Mod’s they are wrong. It doesn’t happen often.
I’m trying to guess the first six British bands to have US hits, rather than the most important bands (i.e., the ones with the most hits or biggest hits or whatever). And I’m not counting the Tornados or any other pre-Beatles British artist.
I would say:
Beatles
Dave Clark Five
Gerry and the Pacemakers
Chad and Jeremy
Peter and Gordon
Freddie and the Dreamers
Other possibilities are Stones, Herman’s Hermits, Animals, or Kinks.
I cheated and went to the Wiki article.
I see more than 6 bands listed there. 
Leaffan, it may not be the same article I am using. I was looking at a specific band and they gave me six names.
Without looking.
The nominees:
-Beatles
-Rolling Stones
-Herman’s Hermits
-Dave Clarke Five
-Animals
-Freddie and the Dreamers
-The Who
-Gerry and the Pacemakers (what a great name for an oldies act)
I’ll go with first six, although the Who will probably bump Freddy in the history articles. I’m pretty sure Freddy had more hits in the early years.
My three guesses (without reading any other responses): Beatles, Rolling Stones, Dave Clark Five