I do not think it a good idea to say only those who can prove they have had the virus can go to work. The government clearly thinks a majority of the population have not had the virus, otherwise they would be relaxing anyway. Limiting going to work to the minority would be unfair and leave the country struggling to pay the bills. The right to work should not depend on a macabre disease based lottery.
Nor do I think it a good idea to have outright bans on people based on age. Of course all those whose age and other medical conditions puts them at more risk from the disease should be protected if they wish. Many will want to be helped to stay at home and avoid potentially dangerous contact. The others should not be placed under house arrest against their will.
The country needs to get back to work, accepting that work patterns will be different. Employees will rightly want safer working methods, including protective clothing where needed, new shift patterns, more homeworking and freedom from congested public transport where the disease might circulate more freely.