The Launcher tries to download the 40.34MB java file and then stops at around 12 MB loaded and starts again. It does this 3 times. For each of them, in the nativelog.txt (attached), they get a 200 from server (OK) and then fail with an operation timeout. After the 3rd try and fail it downloads the launcher.jar (if not already downloaded) which downloads fine. Then tries to launch it and fails as the java.exe obviously hasn't been downloaded.
Out of interest I tried browsing to "http://launcher.mojang.com/jre/win-64/1.8.0_25/bdca00e1c2a1f2c23c9a77b65188b788d475a603/jre-win-64-1.8.0_25.lzma" and the download started in my browser. It downloaded with a few pauses here and there. Therefore, thought is that the timeout coded in the MinecraftLauncher.exe (or whatever tries to download the java) is too short (Maybe only for my network speed).
Also, since I have downloaded the jre-win-64-1.8.0_25.lzma, can I put this somewhere and the launcher unpack it without trying to download another one?