I've never heard of British Seaside mysteries as a genre, and I've been reading mysteries all my (long) life, and I'm British.
(The only one I know of - and highly recommend - is Peter Bartram's
Crompton of the Chronicle mysteries, set in Brighton in the 1950s/1960s and featuring a local crime reporter.)
Whatever - I write British whodunits myself. One series, although contemporary, is listed under Traditional mysteries, female sleuth. For a while, on the insistence of an American author friend, I had it listed under the cozy cat, but a lot of readers have complained. One American reviewer said it wasn't a clean cozy and that the heroine watched two people having sex. Shock! Horror!

It's not so much a sex scene as a sex sentence. The heroine is searching a penthouse office when she hears voices approaching and rushes through the first available door. She listens at the door as two people - possible suspects - enter the office and proceed to get close. When she realises what's about to happen, she hastily closes the door and looks around - only to discover that her sanctuary is the executive bathroom.
The same reader also complained that the book was filled with Hell and damn. It's hardly filled with them - there's a plot and a sub-plot for heaven's sake - but the protagonist's favourite curse is Hell's teeth. Mea culpa on that one.
Another series, set in the 1920s, I've listed under Historical mysteries, female sleuth. (No sex in that one, though there is the occasional damn, dash, and dang. It's the way people talked back then. And some of the characters smoke. They did that in 1924, as well

)
As for your idea of travel mysteries, Lily, check out the books by Judith Cranswick. She writes a series of mysteries featuring a tour guide. They are set in various places in Europe. You might get an idea for covers from them.