I solved my problem.
For me (mid2012 macbook pro 15 retina) it was the handsoff feature.
I turned it off in Settings->General (while turning it off, all ios8 devices and all other macs have to have their bluetooth on)
Now, I am downloading with 3 Mb/s from the same network where moments ago I was not even to load this page fully for several minutes.
I don't know the reason. Is it software? Or maybe the antenna array of Macbook being crammed on the bottom of screen hinge is too much prone to interference when there are too many handsoff devices around? (I have a MacPro + iphone + ipad, two bluetooth keyboards, and two bluetooth mice in "bluetooth range". Just a speculation: maybe with this many things, the older embedded multi frequency antenna design make bluetooth communication bleed into wifi channels? Maybe this is the reason Apple is so silent about it, admitting such a problem will require a costly replacement of probably the whole display unit, since everything tends to be factory bonded together. Also why handsoff keeps on working even when bluetooth is off in the mac? I thought all the communication was via bluetooth. I really don't trust these "software switches" for turning things off)
*edit*: The bluetooth is on at the moment. Turning off bluetooth did not help the problem previously.