The first issue will be is Wales involved as there are restrictions for some moving between England and Wales.
If not Wales and someone were moving between say Bristol where my son is and London where I live - Tier 3 to tier 2 that's allowed as far as I know under the legislation (the guidance is not the law and is not legally binding). If I went to Bristol from London (tier 2 to tier 3) the restrictions to which I am subject move with me you take your local restrictions in England to the tier in which you go.
So for example last night my son had 3 friends in London here for a meal for his birthday outside in the garden in the dark - it was cold, wet and looked really uncomfortable to eat in but they seemed to enjoy it - and those 3 boys did not come in my house as this is tier 2 so they can meet outside but not in (and whether in or out rule of 6 applies across England except for exceptions like work meetings, training, work, school etc).
If he went to Bristol - tier 3 he would still be subject to tier 2 restrictions.
In general the state has made the rules so complicated it is very hard for people to be legally compliant.
These are the tier 2 (London etc) current restrictions www.legislation.gov.uk/uksi/2020/1104/contents/made
Schedule 1 for London etc is all about gatherings www.legislation.gov.uk/uksi/2020/1104/schedule/1/made
This is part of schedule 1 (and I stress this is in the regulations applicable to London and other tier 2). This is the but that says my London son cannot gather with his 3 friends in my house and they eat in the dark in the rain and cold for the good of the nation. (Or supposedly the good of the nation - whether this really helps anyone is yet to be properly proven)....
Participation in gatherings indoors
"1.—(1) No person may participate in a gathering in the Tier 2 area which—
(a)consists of two or more people, and
(b)takes place indoors.
(2) No person living in the Tier 2 area may participate in a gathering outside that area which—
(a)consists of two or more people, and
(b)takes place indoors.
(3) Sub-paragraphs (1) and (2) do not apply if any of the exceptions set out in paragraph 4 apply.
Participation in gatherings outdoors
2.—(1) No person may participate in a gathering in the Tier 2 area which—
(a)consists of more than six people, and
(b)takes place outdoors.
(2) No person living in the Tier 2 area may participate in a gathering outside that area which—
(a)consists of more than six people, and
(b)takes place outdoors.
(3) Sub-paragraphs (1) and (2) do not apply if any of the exceptions set out in paragraph 5 apply.
(4) This paragraph does not permit a person to participate in a gathering in the Tier 2 area in contravention of paragraph 1(2) or 2(2) of Schedule 1 to the Health Protection (Coronavirus, Local COVID-19 Alert Level) (Very High) (England) Regulations 2020. "