Adding to that think another issue with the U.K. is the amount of co-production done here over the last 5 years by HBO with Sky and the BBC... there is a fair amount of programming in the last few years such as Avenue 5, Chernobyl and His Dark Materials
that HBO would not have access to
as the BBC and Sky would naturally want to exploit themselves (And there are still new co-pros coming like The Baby, Landscapers and recently rumoured, Brideshead Revisited with the BBC).
I think you slightly mis-characterized what a
co-production
is .
In what way?
Co-production in the UK usually delivers the UK domestic broadcast and streaming rights for a specified window (3-5 years in most cases) to the UK co-producer, unless unusual deals have been made, and removes those rights from rival streaming services or output deals operated domestically with other outlets/broadcasters within the UK territory.
In most cases UK co-productions with HBO will involve HBO and Sky or the BBC co-commissioning a third party indie (who may also retain some rights in some territories after the BBC's licence period has ended) to make the show, with production input from both commissioning broadcasters over elements such as casting, episode structure, budget, production talent etc.
As the BBC also has a production arm, in some cases the BBC and a third-party broadcaster or OTT operator may co-commission BBC Studios to act as the production arm (distinct from BBC Public Service/BBC Content co-commissioning the production alongside a co-production partner), and BBC Studios (as a commercial arm) may also co-fund some co-pros (separate to BBC Public Service/BBC Content funding). (Good Omens was a BBC/Amazon co-copruduction, produced by BBC Studios for instance. Doctor Who has been a co-production in the past too, made by BBC Studios Wales).
Good Omens was an interesting example as Amazon had negotiated first-run rights on their OTT platform in the UK, with the BBC taking public service rights in a later window in the same territory. This isn't always the case.