The Savoy is a beautifully restored Austrian-era cafe, with smart, suited waitstaff and a Viennese-style menu of hearty soups, salads, roast meats and schnitzels. It's also just a characterful place for coffee and cake and there's a superb wine list (ask the staff for recommendations).
The Savoy is also a good bet for breakfast, with plenty of healthy choices, including a ‘Full English', an American breakfast, and eggs cooked half-a-dozen ways.