//NJ, the power under the Regulation you quoted, applies only to those diagnosed with Covid-19 and self-isolating.
It does not apply to those advised to self-isolate via the English NHS app.//
No it doesn't apply to somebody notified by the app, Corby (presumably because when the legislation was drafted the app couldn't be relied on too much). But it is not restricted only to those who have received a positive diagnosis:
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Requirements on person notified of positive test for acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and close contacts of such persons
2.—(1) This regulation applies where an adult is notified, other than by means of the NHS Covid 19 smartphone app developed and operated by the Secretary of State, by a person specified in paragraph (4) that—
(a)they have—
(i)tested positive for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) (“coronavirus”) pursuant to a test after 28th September 2020, or
(ii)had close contact after 28th September 2020 with someone who has tested positive for coronavirus;
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“close contact” means—
(a)having face-to-face contact with someone at a distance of less than 1 metre,
(b)spending more than 15 minutes within 2 metres of an individual,
(c)travelling in a car or other small vehicle with an individual or in close proximity to an individual on an aeroplane;
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Quite how it is determined (and by whom) that "close contact" as defined has occurred is anybody's guess.
Almost identical restrictions apply to those arriving from abroad, with many places on the "red" list having a much lower infection rate than England.