The exceptions are you may travel to work, it says nothing about travelling to exercise. So you can't do it
That is clearly not the case, as it would not make sense in the context. The full section on restriction on movement reads:
6.—(1) During the emergency period, no person may leave the place where they are living
without reasonable excuse.
(2) For the purposes of paragraph (1), a reasonable excuse includes the need—
(a) 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;
(b) to take exercise either alone or with other members of their household;
(c) to seek medical assistance, including to access any of the services referred to in paragraph 37 or 38 of Schedule 2;
(d) to provide care or assistance, including relevant personal care within the meaning of paragraph 7(3B) of Schedule 4 to the Safeguarding of Vulnerable Groups Act 2006(a), to a vulnerable person, or to provide emergency assistance;
(e) to donate blood;
(f) to travel for the purposes of work or to provide voluntary or charitable services, where it is not reasonably possible for that person to work, or to provide those services, from the place where they are living;
(g) to attend a funeral of—
(i) a member of the person’s household,
(ii) a close family member, or
(iii) if no-one within sub-paragraphs (i) or (ii) are attending, a friend;
(h) to fulfil a legal obligation, including attending court or satisfying bail conditions, or to participate in legal proceedings;
(i) to access critical public services, including [etc]
All these exceptions to the restriction are likely to involve travel. It doesn't specifically say that you can drive to the supermarket or to donate blood, but obviously you can. (f) is referring to travel during the course of your work, as opposed to commuting, e.g. if you're a district nurse. It doesn't mean that you can''t travel for the other reasons listed..