Flying to UK to reset 90-day rule for USA's Visa Waiver Program? [duplicate]

"I am not trying to do a visa run"
What you're trying to do is exactly a visa run, you're leaving and reentering the country with the sole intent of bypassing the limits on your visa.

Why would US immigration believe that you left the country for another reason than to get out from under the 90 day restriction on your visa, or that you aren't planning to stay longer than the 2 weeks you claim?
I know that if I were that immigration officer I'd NOT believe you, deny you entry, and send you packing on the next flight back to London (because that's where you arrived from).

I've heard of others managing this, and it really can come down to the immigration officer, their questions and their belief of the answers you give to said questions.

You're going to want to provide documentation and lots of it. Proof of flight out of the US in two week's time. Proof of your job back home (or study) that you're returning to. Proof of accommodation for only those two weeks. You get the idea. Basically you have to be able to assuage the immigration officer's doubts that you're not just sneaking around the system to stay, and perhaps say, work an under the table job.

So yes, it's possible, but what you're trying to do is and will be viewed as a visa run, and allowing of you back into the States this time (and future times if you get rejected!) will rest on the immigration officer at the time.

Note that if you really want to stay more than 90 days, you could apply for a regular tourist visa, rather than going through the ESTA/VWP system. (see the Australian page for visa applications)