If you go back to the early days of NBC there would be quite a few operating bus companies that didn't take VRTs or VRLs: Tynemouth, Tyneside, Gateshead, Sunderland District, Venture, Hebble, County, Mexborough & Swinton, Thomas Bros, Rhondda, United Welsh, Neath & Cardiff, Stratford Blue.
I think Aldershot & District might have missed-out before its merger with Thames Valley, and possibly the two Bath companies before their absorption by Bristol, and Notts & Derby before its absorption by Midland General. I'm not confident about any of these though. Nor the original Wilts & Dorset - if it did take VRs it might have been just a trading name of Hants & Dorset by then, which I think took place towards the end of the THC era.
Standerwick is an odd one, a coaching company that did take VRs for coaching work.