What is kindest way to stop starlings occupying in the roof-space of my house?

I have lived here 12 years and over last 6 years there has been a variation in the starling population in the "soffings" (eaves or whatever). It is a modern house (1998) and the roof space is well ventilated (not used but lagged). This year I heard a lot of scratching actually in the ceiling area above my home office (now working at home) and think they are inside.

A pest controller visited (i had thought it was mice) and they have told me  there is evidence the starlings are inside the roof space. I have some wire mesh that can "block" the airspace they use to enter but worry about when it is best to do that. Displacing in this cold snap (west yorkshire) feels unkind.

Cheers for any advice,

Mark