The heat wave would have been a factor - although 'only' accounting for hundreds of excess deaths. Reactions to vaccines might have been a marginal factor - although a fraction of the deaths that rampant Covid would have caused.
My educated guess (from reading a lot of opinion and analysis) is that most excess deaths have come from late diagnoses and missed treatments as a consequence of Covid lock-down, overwhelmed hospitals during the height of the pandemic, and the impact of staff vacancies (due to Brexit, stress, long-term illnesses amongst medical staff and inadequate funding).