Windows 10 Anniversary Update fails with error 0xc000000f

I enrolled my machine in the Release Preview ring of the Insider program. The update downloads, prepares to install and then requests a restart. It 'prepares to configure Windows' (I believe), and after the reboot it blue-screens:

Recovery

Your PC/Device needs to be repaired

A required device isn't connected or can't be accessed.

Error code: 0xc000000f

You'll need to use recovery tools. If you don't have any installation media (like a disc or USB device), contact your PC administrator or PC/Device manufacturer.

Press Enter to try again
Press F8 for Startup Settings
Press Esc for UEFI Firmware Settings
Press F9 to use a different operating system

Pressing Enter or F8 just seems to refresh the screen. Pressing Escape leads me to the UEFI configuration screen and F9 returns me to Windows, without having updated. It notifies me afterwards that 'Updates have failed to install'.

The machine has BitLocker enabled, but I'm unsure if that is causing the issue. Also hesitant to disable it, because company policy enforces it.

WindowsUpdate.log doesn't show any meaningful message. A ton of content that seems to indicate success and then:

2016-08-01 09:53:10.8798806 628   1248  Shared          * END * Service exit Exit code = 0x240001
2016-08-01 10:00:43.0283959 628   9832  Agent           WU client version 10.0.10586.494

Which, as far as I can tell, shows one message before the reboot, and one immediately after. Of course there are a lot of messages after the reboot as well. What can I do to either resolve or diagnose this further?

I had the same thing on my HP laptop. Windows couldn't repair itself because of bitlocker.

I did regain access to Windows by starting with my network disconnected. Then I could access a command line an unlock bitlocker using

manage-bde -unlock {-recoverypassword <Password>|-recoverykey <PathToExternalKeyFile>} <Drive>

and then turning it of with

manage-bde -off <Drive>

After rebooting all repair options are available and Windows will be able to reboot. On my pc, logging in with my finger print also stopped functioning correctly so I suspect the problem lies with the TPM, the Trusted Platform Module.

I only succeeded in re-enabling bitlocker after I disabled the TPM module in my BIOS. However, this means it is currently using software encryption, instead of the hardware accellerated version. And I'm still not able to re-enable finger print logon.