The findings come as a union calls for better funding for local BBC services.
Figures for radio listenership are compiled by RAJAR, which carries out an ongoing survey of users based on what stations they listen to, and for how long.
The latest data estimates BBC Somerset reached an average of 66,000 listeners each week in the six months to March.
This was up from around 60,000 in the six months to March 2022.
Over this period the market share of BBC Somerset rose from 2.8% to 4% compared to other available stations.
In October the corporation set out proposals that would see local radio stations share more content and broadcast fewer programmes unique to their areas.
It would mean local programming restricted before 2pm and afternoon programmes across England shared between its 39 local radio stations.
Noel McClean, national secretary of Bectu, a union for the creative industries, said: "We have sympathy for the position it is trying to operate in – but all roads lead back to the need for a properly funded BBC."
Speaking of the planned cuts to local news services, Noel added “a less local BBC is a much-diminished BBC” – and that maintaining services in different areas is crucial for issues such as local democracy.
He said decisions about its future have been driven by short-term thinking and political point-scoring.
Instead, Mr McClean called for an evidence-based review of "what kind of BBC we want, what we want the corporation to do, and how that can best be delivered".
Across the UK, RAJAR figures show weekly BBC local radio listenership fell from around 8.6 million people in the year to March 2022 to 7.4 million this year, with market share dropping from 6.1% to 5.5%.
In the latest survey period the average listener tuned in to BBC Somerset for around 6.2 hours every week – clocking up a total of 411,000 hours weekly.
The Department for Culture, Media and Sport said it "remains disappointed" about plans to reduce local output and has met with BBC bosses to express their concerns.
A BBC spokesperson said: “These figures often fluctuate - particularly for news and community focussed stations such as local radio."
"We have a plan to reach more people with local stories and news across England over the next 12 months."
They continued: “We know audience habits are changing which is why we need to transform what we do to achieve a better balance between our local online and broadcast services. We are committed to reaching more people in more communities across England.”
They added the corporation is committed to retaining local programming and is protecting live local coverage from 6am to 2pm on weekdays.