It comes after the council expressed concerns about the proposals and agreed to lobby the BBC about the changes, which would dramatically reduce the amount of Shropshire-based programming.
This would also see the Shropshire station merge with stations in Stoke and Hereford & Worcester after 2pm on weekdays, and in weekend daytimes.
As well as the corporation's director general, Tim Davie, Councillor Picton has also written to Michelle Donelan, Secretary of State for digital, culture, media and sport, to express the council’s concerns.
She said: “On behalf of the council, I have been clear that we think these proposals will be very bad news for a large, sparse rural county like Shropshire where a healthy local radio station is part of the lifeblood of the county, particularly in times such as floods when people need good local information and reassurance.
“I simply do not believe a station that half the time tries to serve an area from Malpas to Monmouth can effectively do this.
“I hope the BBC will stop these proposals and maintain a more local service."