So you're not in the UK, don't have access to BBC TV and radio, and decide to start a thread called "Have the BBC been asked to limit war coverage" based on what you see on the BBC website?
As someone who is in the UK, I can tell you it's been wall to wall coverage for the past 3 weeks, apart from a brief focus on floods in the UK and the US shooting yesterday. War in Ukraine is hardly mentioned.
The BBC is a broadcaster and the content of their website is secondary to that, unlike newspapers, which are print media and therefore their entire content is visible on their websites.