I have an recent copy of OS Open Borderline and see that not all layers have full coverage (especially in England). I think it really depends on the definition of 'region' you want :)
I don't think it's necessarily a problem with the data, it's more the result of having multiple types of 'region' with different meanings.
If you're looking at some of the Unitary Authority layers, that might explain the gaps in coverage - not all of England is covered by Unitary Authorities (e.g. gaps in the Midlands, Somerset, Isle of Wight etc). The same goes for the "county regions" layer which has similar gaps.
Not too familiar with the intricacies of geopolitical boundaries in England, I'm afraid. This wikipedia article looks as if it might explain the gaps you're seeing.
For other sources, ask on OpenData stackenchange as others have suggested.