The underlying problem is that the Windows Update self-update mechanism is not working. In order to successfully install service pack 1, you need at least version 7.6.7600.256 of Windows Update. Windows Vista RTM ships with Windows Update version 6.0.6000.16386 and at present this version is not able to self-update.
This is happening because the current version of the wuident.cab file (digitally signed July 14, 2012) provided by Microsoft's Windows Update service contains an explicit instruction that versions 6.0.6000 and 6.0.6001 should not attempt to self-update. It is not clear why.
There may be one or more missing files on Microsoft's servers, because error 0x80190194 means that a 404 (File Not Found) error was received from the web server. However, error 0x80190194 does not appear if you are using a WSUS server, but the client will still not self-update. It is possible that the error 0x80190194 is not directly related to the problem.
Microsoft Support advised me that the problem is being worked on and that a KB article will be released in due course. They did not give me an ETA.
In the meantime, there are two ways to solve the problem. Microsoft Support directed me to this download which installs Windows Update 7.6.7600.256. Note however that this is a third party installer not officially supported by Microsoft and personally I do not recommend using it. (For the record, when I tried it, it worked. But that was on a test machine which I then reformatted as a precaution.)
The other is to download and install the off-line version of Windows Vista service pack 1 (or the all languages version) from the Microsoft Download Center. This will take longer to download and install than using Windows Update, but is officially supported.
In either case, once service pack 1 is installed some additional updates will be offered and then service pack 2 will be offered and should successfully install.
Note that Microsoft do provide free phone support for problems installing service packs. See Microsoft's support page for the contact number for your area. Note that in some countries this may be a toll call.