Pressure is growing on Gordon Brown to reshuffle his Cabinet after Thursday’s local elections to take some of the sting out of the drubbing his Labour Party is expected to get at the ballot box this week.

Press reports last week suggested Health Secretary Alan Johnson might be in for a promotion. But government sources show no sign that Brown is about to rearrange the decks just yet.

For a start, it’s not really clear a reshuffle now would sort out the government’s problems. Many of the current Cabinet have such little profile that changing their jobs would hardly excite the public imagination.

Also, the big jobs that might cause a stir are really locked down. Brown isn’t about to remove close ally Alistair Darling from the Treasury — it’d be tantamount to admitting the government bore some of the blame for the economy slowing down. The preferred line is to blame the global credit crunch.

Nor does David Miliband look as if he is going anywhere from the Foreign Office. It wouldn’t make political sense to give the young minister often talked about as a future leader of the Labour Party cause for grievance just when the prime minister’s authority is really under scrutiny.

But Brown still really does need what he calls a “diversion” from all the negative press he’s been getting. His popularity has slumped, the economy is slowing down as house prices fall and his backbenchers are no longer afraid of challenging him on the policy front.

So far his answer has been to say people will back him when they see he’s been taking the right long-term decisions. The economy, he says, will be his main focus.

The problem with that is this is exactly how people remembered him when he was Chancellor of the Exchequer for 10 years. As prime minister, he needs to connect better with voters who are looking for a reason to vote Labour again when the party has already been in office for more than a decade.

Brown doesn’t need to change his Cabinet now, he needs to change the way he communicates.