For the record, I love this idea and have a half written timeline featuring an HP BBC TV series.
The main issues would be these:
Budget, unless specifically produced in the USA, no British Network would have the budget to come close to doing it. A co-production would maybe work, but it would probably require multiple international partners.
For example, Gormenghast was a *MASSIVE* production done in 2000. It was a gold standard at the time and still stands up, but they managed to be efficient by setting it all in a number of sets or minimal location work.
Potter on the other hand, is easily 5 to 10 times the size required. Hogwarts alone would require loads of sets or location work, not to mention Diagon Alley & the Dursleys house etc etc etc.
And anything not cut out would need to be budgeted and paid for.
Experience: Due to the lack genre/sci-fi/horror/fantasy properties on British TV at the time, the production knowledge is either shipped off to a commercial entity or overseas.
The same goes for TV directors & producers who worked with effects, CGI etc, there had been no major, long running show which required extensive effects work, since arguably Doctor Who in 1989 (12 years before hand) and anything which did run was a limited series where the results were.... mixed, at best.
On the other hand.....
Harry Potter was a massive phenomenon in the Anglosphere. It was pretty much a licence to print money before the movies, the movies just kicked it into the stratosphere.
So here is how I made this work in my timeline.
Lets say the BBC get the rights. Now Rowling was fairly smart about the rights, keeping a certain amount of say in them. She demands an all British cast as per OTL. She also turned down an animated version IIRC.
The BBC do a star studded radio version of the first book. Imagine their 1981 Lord of the Rings as a comparison, legendary producer Dirk Maggs & legendary writer Brian Sibley pool their talents to create another "Audio Movie".
This is broadcast in a special afternoon BBC Radio 1 slot during the school summer holidays, similar to their 1990s broadcasts of Batman, Superman & Judge Dredd (all of which are fantastic by the way!)
This is a smash hit, and a second series is commissioned based on the second book to be recorded and broadcast over the nest summer.
The CD & tape cassette sales creates a significant income for the BBC & BBC enterprises which put it toward the basis for a TV series.
So the BBC needs a financing deal to get the rest of the money to do this properly. The broadcast rights will earn a packet. So an agreement is forged with ABC in the US, ABC in Australia, NZBC in New Zealand. BBC worldwide handles sales to non-English language countries. So most of the funding is now in place.
Production would begin in early 2001 with a broadcast date of October 2002 in mind so the series will finish around Christmas time.