If you're all the way in NZ and scarcely watching the BBCs news output you'll perhaps not realise how right leaning it's become.
In the last election they ran tough holding to account interviews with all the party leaders except for Boris. When Boris turned up to the cenotaph on remembrance Sunday hungover and placed his wreath upside down they 'accidentally' showed the wrong tape from another year. When Boris appeared on a question time debate and the audience were laughing at his stupid replies the BBC 'accidentally' edited out the laughter for later news bulletins.
When Labour announced a policy to nationalise broadband provision the BBC called it 'Internet Communism'. They used a Moscow backdrop when discussing Corbyn on the news. When a stressed out dad had a go at Boris in a hospital Kuensberg found his social media and doxxed the poor guy. The day before the election Kuensberg illegally announced on politics live that the tories had done really well with postal votes.
The balance of guests on politics live, newsnight and question time is always 2, 3 or 4 from the right to 1 from the "left". And usually it's someone on the left who's viewpoint is "Labour should move to the right to be electable". When they go through the newspaper headlines on a Sunday the observer gets introduced as "left leaning". No newspaper ever gets introduced as "right leaning".
So no. Its not balanced. Nobody who claims its left leaning will give you any list like the above to evidence why they think it is.