It is good to hear the BBC are taking special care with certain pieces. That isn't the reputation they have for care of props and costumes in the past and it is a change for the better. Someone must have realised that an original Doctor costume is a part of TV history and needs to be valued as such. Even though they are hidden now the BBC still owning them means they could go on public show again sometime [unlike when private buyers get hold of costumes and they are never seen again].
The Pertwee jacket they have must be the Curse of Peladon/Three Doctors one. Pertwee took some jackets with him when he left but that one reappears in the series [in Masque of Mandragora and Time and the Rani and maybe others?]. It has also been on exhibition since then.
This picture is from the Llangollen exhibition which was open in the 1990s - 2000s. The BBC keeping that one does bring back the question of how many of each jacket were made. This is Jon at a convention in 1983.
Jon had a Three Doctors jacket too then by the look of it. Without asking whoever made them I doubt we can ever know how many there were of each jacket. Jon sold off all his jackets so this one will now be in a fan collection somewhere like the purple Planet of the Daleks and green Carnival of Monsters/Time Warrior jackets. Just how many jackets did Jon keep? Here he is in 1977.
The Green Death jacket must be out there in a private collection somewhere too. If the Three Doctors jacket is duplicated then thats at least five original Third Doctor jackets still surviving.
Rust red, stand up collar - BBC
Rust red, stand up collar - private owner
Green - private owner
Purple - private owner
Blue, red trim - private owner
That does leave two often worn jackets [one black and one red] from his first few years unaccounted for plus three of the single use jackets from his final season [blue, green, black].