The simple, additional answer besides "copies of UK", is that more countries have territorial representation than those which are formal federations. An example would be Spain--it has 17 autonomous regions (+2 such cities), but it's not a full-fledged federation. Basically, there's a spectrum of decentralization.
Slightly longer answer, based on one of those sources is that the reasons have been sometimes pegged into 4 categories:
Chambers of review and reflection. They exist to improve the quality of
legislation and to provide a forum in which appointed experts and elder
statespersons can debate the technical details of legislation in a calm,
informed manner, without challenging the primacy of the lower chamber
in terms of policymaking. The members of such a chamber would mainly
be recruited from within political, legal and administrative elites, and their
powers might be limited to proposing amendments and delaying
Chambers intended to provide territorial representation. These occur
especially in federal systems, serving to protect the right and interests of
the territorial units and to give them a say in legislation. Such chambers
might be directly elected on a territorial basis, or chosen by the
subnational legislatures, and they might have fairly extensive veto powers.
Chambers which exist to provide breadth of representation. This can be
achieved either by including certain minority communities or by giving an
institutional voice to certain social, economic and cultural interests.
Chambers based on the principle of democratic contestation. Such chambers
provide a democratic check on incumbents. Second chambers in this last
category are necessarily chosen by direct election (often using a different
electoral system and/or electoral cycle to that used by the primary
chamber) and might typically possess extensive veto powers.
Of course, these categories are not mutually exclusive, and in reality many
second chambers play two or more complementary roles (see Table 4.1)
According to that source, there are some countries where the two
chambers are practically duplicates of each other though. The example
provided there is Romania. Looking through the Wikipedia article of that country's senate, it seems that in older constitutions their senate had seats for clergy etc., which in some sense copied the UK system, but there's no clear reason given why the senate was reconstituted in later times/constitutions. I guess it may have been because Romania has a semi-presidential system fairly inspired from France's which also has a Senate, but France's is elected indirectly, whereas Romania's is directly elected. (Aside: Romania's president has less powers than France's.) So I guess besides "UK copies", there are "France copies" as a tradition-type reason.
Somewhat (but not directly) related, there is actually an interesting paper that proposes that a concept of "semi-parliamentarism" justifies a 2nd chamber; this is defined as:
- There is no direct (or popular) election of the chief executive or head of state.
- The assembly has two directly elected houses.
- Only the lower house can dismiss the cabinet in a no-confidence vote.
- The upper house has veto power over ordinary legislation that is not merely suspensory and/or cannot be overridden by a simple or absolute majority in the lower house.
The core features of semi-parliamentary bicameralism are conditions (2) and (3): even though the upper house is directly elected, it does not participate in the no-confidence procedure.
Defined this way, this system is mutually exclusive with a semi-presidential one, because of condition 1. (The term "semi-parliamentary" term alas has had other definitions.)
According to the author of that paper, a not-strictly-federal country that qualifies for that definition of semi-parliamentarism is Japan.