Microsoft has recently confirmed that an official fix for the Windows RT update bug would be released in early February, but a Surface support team member found a workaround that seems to fix the issue in some cases.
Basically, it all comes down to this app troubleshooter that needs to be downloaded on an affected Windows RT device.
Steven_B recommends users to run the Troubleshooter on the tablet and press “Next” even if the app states that it doesn’t work for ARM devices. Complete the wizard and reboot the Surface.
While this workaround seems to fix the Windows Store, those who wish to regain access to Windows Update need to launch the “Troubleshooting” option in Control Panel, touch “Windows Update,” hit “Next,” and “Try troubleshooting as an administrator.” Close the app and then reboot the device.
This trick should do the job for the affected Windows RT devices, at least temporarily until Microsoft releases the long-awaited patch.