The new statistics, revealed in an Office for National Statistics report, take into account deaths in care homes and the community.
The death toll from coronavirus was 41 per cent higher than the figure in the daily total released by Government based on hospital reports.
The number of weekly deaths in care homes has doubled to 2,456 since the first Covid-19 related deaths were registered in the England and Wales.
The ONS data collects all deaths related to coronavirus, including those in care homes, hospices and at home. As a result, it has significantly increased the disease’s overall death toll up to 11 days ago.
The provisional number of deaths registered in the week is 2,129 higher than the previous week, and 7,996 higher than the five-year average for the week – meaning that almost 8,000 more people died than might statistically be expected for the time of year.
Of the 18,516 deaths, 33.4 per cent included a reference to Covid-19 in the registration, meaning that the virus may directly have contributed to 6,213 additional deaths.
In London, which has been hit hardest by the outbreak, more than half of all death registrations mentioned coronavirus, while in the West Midlands, which has also suffered heavy impact, the number is above the national level at 37 per cent.
There were no coronavirus deaths among those aged 14 and under in the week in question, with the number increasing through the age brackets and peaking with victims aged between 75 and 84.
The death rate continues to be higher among men than women, most markedly in the 75-to-84 age bracket. This is consistent with expectations based on data from elsewhere, including the early WHO study in China.
The doubled rate of deaths in care homes is accompanied by an increase in proportion of deaths, up from 22.4 per cent of total deaths before the first coronavirus fatality to 26.6 per cent of all deaths now.
The ONS will begin to publish data on care home deaths from coronavirus specifically from 28 April on, it said in its summary.
The report only covers England and Wales for now, although Northern Ireland and Scotland could be included in data in the future.
