I think /ɒ/ as in not, hot, cot in BrE is the counterpart to /ɔ/ as in call, ball, hall in AmE.
I watched the video of /ɒ/ pronunciation, and it was showing making round lips to make the sound, which is similar to American /ɔ/.
For both /ɒ/ and /ɔ/, do they actually round their lips or in many cases, just pronounce it simiar to schwa /ə/? If you speak fast, you wouldn't make a difference between /ɒ/or /ɔ/ and /ə/, as rounding lips would reduce speech speed.