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Both the UK and Scottish governments have stressed the importance of testing but differences have emerged in the detail of who should be prioritised.
In both countries, all hospital patients who are suspected of having Covid-19 are tested.
In Scotland all patients over 70 who are admitted to hospital for any reason will now be tested on admission, with tests repeated every four days.
But in England testing is being rolled out to all NHS or social care staff and residents in care homes regardless of whether or not they are showing symptoms.
The UK government says it is piloting sending packages of "satellite" test kits directly to care homes across England to enable testing of residents.
Currently Scottish care home residents are offered testing if they have Covid symptoms and all patients entering care homes are tested at least once, according to the Scottish government.
Scottish Care, which represents the independent care sector, would like to see a significant ramping up of testing in care homes, with all staff and residents tested when there has been a case of Covid-19.
The first minister has signalled that more changes to the testing strategy in Scotland will be announced shortly as capacity increases.
Who else can get a test?
Anyone aged 65 or over in England who has symptoms can now apply for a test via the UK government's testing application website.
Testing south of the border is also available for anyone with symptoms who cannot work from home - for instance construction workers, emergency plumbers and delivery drivers.
Unions have been calling construction workers to be tested because so many have kept on working through the lockdown.
Both the UK and Scottish governments have for some time prioritised NHS and other frontline workers who have symptoms as well as members of their household.
In England, these "essential workers" include those working in the military, police, prison service, education and childcare, social work, transport, the food sector, local government, utilities and energy, banking staff, journalists, the funeral industry and religious staff.
The Scottish government has set out its own "priority matrix" for testing of key workers, dividing them into four groups. These workers and their household members can apply for testing only if they are showing symptoms.
- Priority Group 1: Health and social care workers; staff working in residential institutions and essential roles where service resilience is at risk.
- Priority Group 2: Essential workers in critical national infrastructure fundamental for safety and security, and life-line services.
- Priority Group 3: Staff directly involved in delivering other essential services.
- Priority Group 4: Staff involved in volunteering, or in nationally or locally significant industry important to economic sustainability and growth
How do you access these tests in Scotland?
Two systems are running in parallel - NHS testing and testing under the UK Government Testing Programme.
Those in the top priority group are mainly tested using NHS facilities using a referral system.
Other groups can also access these tests but if there's no capacity they can also apply for a test under the UK government programme, using its test booking website.
Drive-through testing is available under this programme at Glasgow Airport, Edinburgh Airport, Inverness (at the Highland and Islands University Campus) and at Aberdeen Airport. A site in Perth will open later this week.
You can access these centres if you live within a 90-minute drive.
Work is under way to roll out smaller and mobile testing facilities as well as home test kits. The UK government says 13 mobile test units will be operated by the military in Scotland.