Sir Simon Wessely of King’s College, London is a well known British psychologist and a member of the government’s special scientific advisory committee. Appearing on the BBC program The Week in Westminster (16 May 2020), Wessely said the new slogan was problematic, since people won’t know specifically what to do:

The message of stay at home is clear. The message of stay alert is not clear at all. I have no idea genuinely what that means. Half the population are already exceptionally alert and need no reminding to be alert. And indeed as time goes on, we will find that message is actually counter-productive.

Good messaging in previous public health campaigns, and that’s what we’re talking about–like don’t drink and drive–it tells you not how to feel–don’t panic, stay calm, stay alert– but it tells you what you should do, why you should do it and how you should do it.

Stay Alert doesn’t carry any of those characteristics.

Sir Simon Wessely, Week at Westminster Podcast, 16 May 2020

The entire Week In Westminster Podcast can be found here:

https://www.bbc.co.uk/sounds/play/m000j7gc