This petition was rejected

The Government e-Petitions Team gave the following reason:

The opening arrangements for supermarkets are a matter for individual retailers, not the Government or Parliament. A number of retailers have announced plans to open early for key workers. You should contact your local supermarket to find out if they have put such arrangements in place.

The Government has made certain changes to enable supermarkets to work together during the coronavirus outbreak, particularly to serve customers who are key staff, elderly, ill or vulnerable: 
www.gov.uk/government/news/supermarkets-to-join-forces-to-feed-the-nation

You can find out more about coronavirus and how you can protect yourself and others here:
www.gov.uk/coronavirus
www.nhs.uk/conditions/coronavirus-covid-19/

You can read NHS tips to help if you are worried about coronavirus here: www.nhs.uk/oneyou/every-mind-matters/coronavirus-covid-19-anxiety-tips

You can read impartial analysis of the Government response to coronavirus and policy developments here:
commonslibrary.parliament.uk/coronavirus/

You may also be interested to know that because of the large number of petitions that have been started in relation to coronavirus, the Petitions Committee has been questioning the Government about its response to the coronavirus outbreak.
 
Find out more and watch the Committee put questions suggested by petitioners to Government Ministers and the Deputy Chief Medical Officer: committees.parliament.uk/committee/326/petitions-committee/news/145767/committee-question-deputy-chief-medical-officer-and-ministers-on-coronavirus-response/
 
Read letters asking further questions of Government Ministers: committees.parliament.uk/committee/326/petitions-committee/publications/3/correspondence/