There is a binary patch for Qt5Network.dll available that enabled buffering of the TCP Socket:
http://bugs.winehq.org/show_bug.cgi?id=31438#attach_47911
Just do as the comment says. Download the file as Qt5Network.bin.patch into the Origin directory (where the Qt5Network.dll file is located).
Change in the directory and run the command:
patch -p0 < Qt5Network.bin.patch
Should just output: patching file Qt5Network.dll
This should fix problems regarding the download speed in origin.
Just downloading Dead Space+Mass Effect with 6MB/s.