I didn't think the edited version posted on youtube reflected too well on either party.
ATCO Annie was being a bit intrusive, labouring the point how many times she had told him to clear the runway (she lost count eventually ) & drawing out the conversation so long that she was indeed negating his ability to carry out a checklist (which many operators do whilst lining up as SOP's not personal preference on the day.)
Whilst in full agreement that Nige should have cleared the runway when told, rather than employing delaying tactics, the whole thing deteriorated into a bit of a "personal" bun-fight right at the stage that he seemed to be going, by Miss ATCO starting to labour the point again vis a vis his refusal to comply (leave that for the report over a coffee on your next break love )
Without hearing the transcript of what took place before, and how/whether BA stated their readiness on ground freq + the alleged silence "breaks", I think the only conclusion we can draw is that this "situation" was not handled in a very optimum fashion by all concerned.
Seems the youtube OP may have had some axe to grind, either nationality or BA based.