The Government/NHS advice is to stay at home if you have symptoms that
might be leading towards full-blown Covid-19 symptoms.
So if you've simply got a high temperature (even though you don't feel particularly unwell) or a newly-developed continuous cough (even though you've got no other cold/flu symptoms at all), you should still remain at home for 7 days:
https://www.nhs.uk/conditions/coronavirus-covid-19/
Many (probably most?) people would normally continue to go to work and/or socialise with others if they'd simply got 'an annoying cough' (rather than 'flu'). It's those people to whom the advice to self-isolate is mainly aimed at.