Thanks for the photo.
I'm afraid your new BDR91 requires a permanent Live and Neutral connection.
As you've said, your existing stat is 2 wire, having a live and switched live, going back to the boiler.
The cable feeding it is also 2 core and earth - there isn't a spare core that could provide a neutral.
Ideally, you would have a 3 core and earth flex, connected back to the boiler.
Also unfortunately, Worcester in their wisdom, hide the wiring connections behind the cover that forms part of the boilers room sealng. After accessing the wiring connections, the boiler should be checked for safety by a gas fitter.
Does the wiring to the stat pass anywhere near the boilers fused connection unit?
If it does, it may be possible to provide a permanent live and neutral from there.
Is there a separate programmer used for timing the heating?