This (non peer-reviewed) study out of Rockefeller University is the only one I could find dealing with this issue.
I’m not an expert so can’t confidently interpret their language, but it seems to be saying that the effects of the new strains (UK, SA, Brazil) on general vaccine efficacy is fairly modest due to these vaccines’ polyclonal effects. I think Hancock might be confused between the new variant’s effect on the vaccine in general and its effect on certain antibodies that the vaccine provokes. Study abstract says:
Here we report on the antibody and memory B cell responses in a cohort of 20 volunteers who received either the Moderna (mRNA-1273) or Pfizer-BioNTech (BNT162b2) vaccines. Consistent with prior reports, 8 weeks after the second vaccine injection volunteers showed high levels of IgM, and IgG anti-SARS-CoV-2 spike protein (S), receptor binding domain (RBD) binding titers3,5. Moreover, the plasma neutralizing activity, and the relative numbers of RBD-specific memory B cells were equivalent to individuals who recovered from natural infection6,7. However, activity against SARS-CoV-2 variants encoding E484K or N501Y or the K417N:E484K:N501Y combination was reduced by a small but significant margin. Consistent with these findings, vaccine-elicited monoclonal antibodies (mAbs) potently neutralize SARS-CoV-2, targeting a number of different RBD epitopes epitopes in common with mAbs isolated from infected donors. Structural analyses of mAbs complexed with S trimer suggest that vaccine- and virus-encoded S adopts similar conformations to induce equivalent anti-RBD antibodies. However, neutralization by 14 of the 17 most potent mAbs tested was reduced or abolished by either K417N, or E484K, or N501Y mutations. Notably, the same mutations were selected when recombinant vesicular stomatitis virus (rVSV)/SARS-CoV-2 S was cultured in the presence of the vaccine elicited mAbs. Taken together the results suggest that the monoclonal antibodies in clinical use should be tested against newly arising variants, and that mRNA vaccines may need to be updated periodically to avoid potential loss of clinical efficacy.
Their conclusion seems to be that while current mutations don’t escape the current vaccine, their evolutionary trajectory seems to indicate that they eventually will and that vaccines may have to be tweaked in the future:
A number of circulating SARS-CoV-2 variants that have been associated with rapidly increasing case numbers and have particular prevalence in the UK (B1.1.7/501Y.V1), South Africa (501Y.V2) and Brazil (B1.1.28/501.V3)12,15,17,28,39. Our experiments indicate that these variants, and potentially others that carry K417N/T, E484K and N501Y mutations, can reduce the neutralization potency of vaccinee plasma. The comparatively modest effects of the mutations on viral sensitivity to plasma reflects the polyclonal nature of the neutralizing antibodies in vaccinee plasma. Nevertheless, emergence of these particular variants is consistent with the dominance of the class 1 and 2 antibody response in infected or vaccinated individuals and raises the possibility that they emerged in response to immune selection in individuals with non-sterilizing immunity. What the long-term effect of accumulation of mutations on the SARS-CoV-2 pandemic will be is not known, but the common cold coronavirus HCoV-229E evolves antigenic variants that are comparatively resistant to the older sera but remain sensitive to contemporaneous sera40. Thus, it is possible that these mutations and others that emerge in individuals with suboptimal or waning immunity will erode the effectiveness of natural and vaccine elicited immunity. The data suggests that SARS-CoV-2 vaccines may need to be updated and immunity monitored in order to compensate for viral evolution.