I depends what you mean by 'effective'.
No vaccines are 100% effective, so if there are large numbers of infected people around (for example the 800 or so per 100,000 teenagers who are positive for Covid right now in Bolton), then even vaccinated people will catch Covid.
A small percentage of these will become very ill, especially remembering that the vaccinated at the moment include the very vulnerable and those, such as the elderly or immunocompromised, most likely to develop relatively low immune response to the vaccine.
A small percentage of those will die.
Those small percentages are not important when overall numbers of cases are extremely small - if cases were down in the numbers for e.g. measles, in the hundreds per year - because they translate into extremely small absolute numbers.
If cases go back up to the 80,000+ levels (5 doubling times from the current position), then those small percentages will still translate into large absolute numbers. Remember that a significant number of people are not yet vaccinated - or fully vaccinated, as that seems to be what is necessary to bring protection up to s decent level against the new variant - and so could easily get those case numbers right up again, thus enabling 'breakthrough' infections in those who are vaccinated but do not have a robust response.