[Keith]

Reading between the lines sounds like has quit because he doesn’t like some of the changes to Radio 2 going on.

Worth baring in mind that his current Radio 2 salary is published in the BBC's yearly salary list, which may or may not be a factor in it.
From reading www.bauermedia.co.uk  it looks like his new show will be weekdays 10am to 1pm, so it doesn't look like he's wanting to cut back his hours now he's 71.

I wouldn't be too surprised if BBC / Radio 2 use his departure as an opportunity to rejig the morning schedules, so that the replacement doesn't have a 9.30am to midday slot. That way the replacement can potentially be on a different/lower salary in relation to hours presenting, without it being too easy to compare and claim they're being paid less.