This is a comedic play on the words 'Southern Comfort', which can refer to several different things.
At its most straightforward 'A Touch of Southern Comfort' sounds welcoming and warm. However, in the UK there is an unofficial 'north-south divide', with northerners and southerners mocking and ridiculing one another. Southerners (e.g. from London) joke about the starkness of the northern climate and the austerity of its people, hence the expression 'it's grim up north'. Northerners (e.g. from Yorkshire) mock the 'soft' and pampered southerners who can't seem to get by without their daily luxuries.
So a wine bar in Yorkshire that calls itself 'A Touch of Southern Comfort' is mocking either the north with its starkness, or (more likely) the inability of southerners to get by without the luxuries of home. Or possibly both.
Another interpretation of the phrase is that it refers to the (southern) genital area, and that 'southern comfort' means sexual activity. The bar may, or may not, be a gay bar: we have to keep guessing.
Southern Comfort is also an alcoholic drink: a type of whisky liquor.