Under the test and trace system that launched on 28 May, a person who has been notified that they have had contact with a person with coronavirus is requested to self-isolate for 14 days. The rules relating to SSP have been amended to include employees who are self-isolating in these circumstances.
If you have been working from home and are not furloughed, you may be able to continue working and should receive full pay, as normal. If this does not apply and your employer does not have a company sick pay scheme, then under new laws from 28th May 2020, you may be entitled to receive SSP for every day you are in isolation - from the first day - as long as you meet the eligibility conditions. This is the case whether or not you go on to develop symptoms.
If you were already on furlough when you were contacted by the test and trace service, you should discuss with your employer whether it is best for you to be kept on furlough or moved over to SSP - although there seems to be some flexibility, you cannot receive both at the same time. One consideration is that employers are required to pay SSP themselves, although may qualify for a rebate for up to two weeks of SSP. If employers keep a 'sick' furloughed employee on furlough, they remain eligible to claim at least a proportion for these costs through the furlough scheme.