Wasn’t News 24 Sunday before The Andrew Marr Show? I have a vague memory of it being on in the run up to something new starting.
Yes, News 24 Sunday was the programme that ran in the summer of 2005 between Breakfast With Frost ending and Sunday AM, as it was initially called, beginning. It was presented by Peter Sissons from the News 24 studio and included interviews and a paper review, certainly more of a programme than just an hour of news. It also ran in the summers of 2006 and 2007 while Andrew Marr was on holiday, but it struck me as a bit odd in that it was simulcast on News 24 but Andrew Marr wasn't, and I didn't know why they didn't just carry on The Andrew Marr Show but presented by Peter Sissons - which is what they then did.
For a few months in 2003 there was also a short-lived politics strand on Saturday mornings on BBC2. This was the result of the same review of the Beeb's political output that saw Westminster Live and On The Record replaced by Daily Politics and The Politics Show, and introduced This Week. One other aspect was an attempt to launch a political programme aimed at younger audiences, so two short-lived series - The Sharp End with Clive Anderson https://genome.ch.bbc.co.uk/schedules/bbctwo/england/2003-10-04#at-9.15
and Weekend with Rod Liddle and Kate Silverton https://genome.ch.bbc.co.uk/schedules/bbctwo/england/2003-05-10#at-9.00
(I know it seems bizarre that Liddle was considered a draw for young people, but it was a while back) - ran on Saturday mornings on BBC2 that were supposed to be a bit more irreverent. But nobody watched either so that experiment was swiftly dropped.
There was also another ill-advised venture on Saturday mornings in the summer of 2004 called In The Know which was simulcast on BBC1 and News 24 and was a live sports magazine with John Inverdale and Louise Minchin, mixed with the usual News 24 hour, which was a bit of a disaster - https://genome.ch.bbc.co.uk/schedules/bbcone/london/2004-06-12#at-9.30