@Hearhoovesthinkzebras
It doesn't define a reasonable excuse and health reasons are a justifiable reason for travel anyway
It gives a list of what a reasonable excuse includes.
There may be other reasonable excuses available - but I don't think going to a 2nd home is a reasonable excuse, even if it's not on the list.
Restrictions on movement
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(1), 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—
(i)childcare or educational facilities (where these are still available to a child in relation to whom that person is the parent, or has parental responsibility for, or care of the child);
(ii)social services;
(iii)services provided by the Department of Work and Pensions;
(iv)services provided to victims (such as victims of crime);
(j)in relation to children who do not live in the same household as their parents, or one of their parents, to continue existing arrangements for access to, and contact between, parents and children, and for the purposes of this paragraph, “parent” includes a person who is not a parent of the child, but who has parental responsibility for, or who has care of, the child;
(k)in the case of a minister of religion or worship leader, to go to their place of worship;
(l)to move house where reasonably necessary;
(m)to avoid injury or illness or to escape a risk of harm.
So I can't really see going to a 2nd house is reasonable excuse - even if it is for 'health reasons'.
Where as going for exercise is fine.