As per my long post above, most virologists don't think any of the variants, including the UK one, will be less susceptible to the vaccine response, but eventually (probably in a few years, not tomorrow), there may be some cumulative set of mutations that lead to reduced vaccine efficacy. The BioNTech CEO also reassured people today that the new variant is very unlikely to "escape" the vaccine (and they were the ones who invented the mRNA vaccine, not Pfizer).
https://www.reuters.com/article/us-health-coronavirus-britain-biontech-idUSKBN28V2M3
The good news there, as per that tweet thread I posted, is that once a new variant has been sequenced, especially in the RBD (receptor binding domain - spike protein, which is what the vaccines target), developing a new mRNA sequence (for mRNA vaccines, like Moderna/Pfizer) or for spike protein carrying viral vectors vaccines (like Astra-Zeneca/J&J) or complementary protein/antibody vaccines (Novavax) to attack that new sequence should not be that difficult to develop and roll out in several months, like is done for the flu every year (without repeating all the clinical trials - for CV, a phase III repeat vs. the existing vaccine, might be required - not sure).
These updates should also be much easier to implement with these vaccines than they are with flu vaccines. The Times article below summarizes this and many other issues with this new variant well. The bottom line, to quote Kevin Bacon's character in Animal House, is "remain calm!"
https://www.nytimes.com/2020/12/20/health/coronavirus-britain-variant.html