Here are some local history publishers in the UK that specialize in publishing books on regional cookbooks and food histories:
Grub Street Publishing: They specialize in food and drink books, including regional cookbooks and food histories. They accept submissions from both established and new authors.
The History Press: They publish books on local and regional history, as well as travel guides. They accept submissions on regional cookbooks and food histories and have a dedicated team that works with authors to help them through the publishing process.
Prospect Books: They are a publisher that specializes in food and drink books, including regional cookbooks and food histories. They accept submissions from both established and new authors.
The National Trust: They are a British conservation organization that also publishes books, including regional cookbooks and food histories.
The British Library: They are a national library of the United Kingdom and the largest library in the world by number of items catalogued, they also have a publishing arm and sometimes they accept submission, it's worth checking their website for more information.
The History Press Ireland: They focus on publishing local and regional history books in Ireland and accepts submissions on regional cookbooks and food histories and have a dedicated team that works with authors to help them through the publishing process.
The History Press Scotland: They focus on publishing local and regional history books in Scotland and accepts submissions on regional cookbooks and food histories and have a dedicated team that works with authors to help them through the publishing process.
The History Press Wales: They focus on publishing local and regional history books in Wales and accepts submissions on regional cookbooks and food histories and have a dedicated team that works with authors to help them through the publishing process.
It's also worth checking local libraries, historical societies, and independent bookstores in the region you're interested in writing about for additional resources and potential publishers. Additionally, many food and drink societies in the UK also have their own publishing arms, and it's worth checking their websites for more information.