Unfortunately government "guidance" and police policy changes rapidly and is inconsistent, especially as the Regulations are made under health legislation, which is now a devolved matter so the four UK jurisdictions (England, Wales, Scotland, Northern Ireland) all have similar-but-different rules and guidance.
In terms of what exercise is reasonable, the Govt has issued guidance in a different context. (my emphasis)
• Adults should do activities to develop or maintain strength in the
major muscle groups. These could include heavy gardening, carrying
heavy shopping, or resistance exercise. Muscle strengthening
activities should be done on at least two days a week, but any
strengthening activity is better than none.
Professor Dame Sally C Davies, Chief Medical Officer, England
Dr Frank Atherton, Chief Medical Officer/Medical Director NHS Wales
Dr Michael McBride, Chief Medical Officer, Northern Ireland
Dr Catherine Calderwood, [then] Chief Medical Officer, Scotland
https://www.gov.uk/government/publications/physical-activity-guidelines-uk-chief-medical-officers-report
Police guidance, which may not always be followed by individual officers, has changed.
New guidance has been issued by the National Police Chiefs’ Council
and the College of Policing
Police forces have been told people should not be punished for
travelling a “reasonable distance” to exercise following criticism of
heavy-handed tactics used to enforce the Covid-19 lockdown.
The new guidance, issued by the National Police Chiefs’ Council (NPCC)
and the College of Policing on Tuesday night, also states road checks
on every vehicle are “disproportionate”.
It comes after Derbyshire Police faced a backlash for filming walkers
with drones to deter visitors to the Peak District, while North
Yorkshire Police stopped motorists at “checkpoints” last week.
The new guidance states: “Use your judgement and common sense; for
example, people will want to exercise locally and may need to travel
to do so, we don’t want the public sanctioned for travelling a
reasonable distance to exercise.
It says: “There is no power to ‘stop and account’. The police will
apply the law in a system that is flexible, discretionary and
pragmatic.
https://www.plymouthherald.co.uk/news/uk-world-news/people-can-drive-reasonable-distance-4006925
The difficulty is, of course, that if you refuse any fixed penalty (initially £30) it will go to court; the government will be represented by an experienced prosecution barrister and you will probably have a solicitor or very junior barrister, at your own expense. Legal Aid is restricted in availability and only covers very low rates of legal fees. Already one person has been prosecuted for an offence that does not exist and the police (British Transport Police) have apologised and asked for the conviction to be reversed.
The prior and detailed answer by Aurora0001 does not address the question:
Is the reasonable excuse of exercise in 6(2)(b) further qualified by any sense of "reasonable", or, once the purpose is given as "exercise", is that then a permitted purpose without restriction?
The legislation is badly written and is being misrepresented by police, government, and much of the media.