The one and only original: HP Sauce. It's the only brown sauce worth using. A-1 is no competition at all.
However, I really don't use "steak sauce". Due to my Irish upbringing, I call it brown sauce, and I put it on all kinds of things, but not steak, because good steak needs no condiments, and I don't waste my money on bad steak. (If I buy cheaper cuts of beef, I slow-cook them in a liquid.)
Brown sauce is especially good with smoked pork products, such as sausage and bacon. It's also really great on pan-fried potatoes. For those reasons, brown sauce is a breakfast staple in Ireland and the UK.
BTW, what you might call the "official sandwich" of the north of England is the bacon buttie, which consists of a soft roll, lean bacon (what Americans think of as Canadian Bacon), and lashings of HP. Yummy. (Fattening, of course, but worth the occasional splurge.)