I dunno if you know the big ones already, plus I have no concept of what from the US makes it over to the UK, so maybe "big" is a relative term.
Anyhow in the current DIY scene, I'd say it's pretty safe to say that the standard bearer is Razorcake. They cover all genres associated with punk, have some good writers and interviewers on their staff and generally appeal to the Fest-crowd's brand of punk rock, and are very much in-touch with the bands that are touring basements today that people really care about:
Razorcake/Gorsky Press, Inc.
PO Box 42129
Los Angeles, CA 90042
Then of course you have Mamimumrocknroll or MRR. Kinda like the daddy of Razorcake, who used to be cool but is kinda out of touch. MRR is basically the old war horse of American punk zines and its name still commands respect, and they still run some awesome shit, but at the same time, half the time you get shit-for-brains reviewers who write complete nonsense. For instance, when the last Degenerics 7" (New Jersey blistering politico-punk) came out, MRR, which would have creamed its collective jeans over the Degenerics in the 80s, ran a review of it that knocked it for being jockish hardcore...which is, ummm, absolutely impossible if you listen to the record. Anyhow, just chalk it up to an old zine getting crazy in its old age, just like your grandpa did, and you'll probably wanna have a review in MRR for better or for worse:
PO Box 460760
San Francisco, CA 94146-0760
Then we have Punk Planet. Punk Planet is thick, its covers are heavy paper stock, and it's expensive! They don't have the tongue in cheek underdog sense of humor of many aspects of the above zines, but it's generally a pretty damn good read, and they tend to have as much about politics and society as about music (but in a good way, generally). They cover a lot of more indie-rock flavored punk, but they cover all kinds of punk, so you'll probably wanna submit to them, too:
4229 N. Honore
Chicago IL 60613
Sadly, you can't submit to HeartattaCk anymore, which was always fun because they would refuse to review anything with a barcode on it. But they're done.
Oh and as far as online stuff goes, make sure you submit to http://www.pitchforkmedia.com/
so as to ensure that a bunch of screamingly self-important, pretentious pieces of shit fall over themselves to find the snarkiest way possible to prove that they are smarter than your record.