@Xenia that's correct. You cannot leave home except with reasonable excuse, which includes 'exercise' without further qualification, so the police have very limited legal grounds to stop that.
Shopping is a bit more restricted as the law says
"to obtain basic necessities, including food and medical supplies for those in the same household (including any pets or animals in the household) or for vulnerable persons and supplies for the essential upkeep, maintenance and functioning of the household, or the household of a vulnerable person, or to obtain money, including from any business listed in Part 3 of Schedule 2;"
It is not clear what 'essential upkeep, maintenance and functioning of the household' means. Presumably going to B&Q to buy bathroom paint would not qualify.
However the restriction is on leaving the house without reasonable excuse, so if you went to B&Q to get some tiles to fix your leaking roof then that would be a reasonable excuse, and there is no restriction on what you do when you are in B&Q.
Likewise it seems that 'basic necessities' is extremely broadly construed given that the list of essential businesses includes
' Off licenses and licensed shops selling alcohol (including breweries).'
If you can go to the brewery to buy beer, then Gary can go to the newsagent (also an essential business) to buy a packet of crisps, just as Fred can buy his copy of The Sun. All these journeys are entirely lawful.
It might be considered antisocial or immoral to go shopping five times a day, but it is not illegal.