Why are the first three seasons of the Great British Bake-Off missing on Netflix USA?

Note: I am assuming from your question that you are based in the USA, and the answer below is based on this assumption. The answer below also contains some conjecture, but given the secretive and byzantine nature of most streaming/airing/export arrangements, I suspect this is as close of an answer as we're going to get using public knowledge.

Note 2: This answer was revised substantially in Fall 2021 to better reflect the airing details after 2018.

The Great British Bake-Off, like many BBC imports, was originally aired in the US on PBS. PBS began airing the show in early 2015, after the highly popular fifth series aired in the UK:

The October finale was 2014’s second most watched TV program in the U.K., bested only by the England-Uruguay World Cup match.

However, by that point the show had been airing in the UK for some time. In its first few seasons, it was not nearly as popular; the first series only had about one-quarter of the viewership of the fifth series. Given these viewership numbers, it is understandable that PBS decided to air the more recent, more popular, and more "matured" Series 5 as "Season 1" in the USA, rather than airing Series 1. (By "matured", I simply mean that the format of the first series was rather different than the format later on.)

Subsequently, PBS aired Series 4 as "Season 2", Series 6 as "Season 3", and Series 7 as "Season 4". Finally, in summer 2018, PBS aired Series 3 as "Season 5".

Netflix originally streamed GBBO via an agreement with PBS, so they numbered the above "seasons" from PBS the same way that PBS did (calling them "collections" instead.) When GBBO moved from the BBC to Channel 4, PBS did not renew its deal to air subsequent seasons; all of the "Channel 4" series, created in 2017 onwards, have aired exclusively on Netflix in the US. Since that time, Netflix has continued to stream each season of GBBO/GBBS in the US roughly contemporaneously with its UK airing, usually releasing each episode a few days after it airs in airs in the UK. The numbering has consistently been offset by 3, e.g., Series 9 in the UK corresponds to Collection 6 on Netflix US.

Series 1 and 2 of The Great British Bake-Off have not aired in the US. It seems plausible that PBS has the rights of "first airing" in the US for Series 1–2 of The Great British Bake-Off. This would make sense given the long-time business relationship between PBS and the BBC. Netflix would likely have to strike some kind of deal with the BBC or PBS to air these two series. Given that the series in question are over 10 years old at this point, this seems unlikely to me; but you never know.

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