See also Category Greasy Spoons for all your death-by-cholesterol fried breakfast requirements.
There's a couple of good meaty restaurants near Smithfields, unsurprisingly. However I need to tap the brain of someone who knows more about them than me.
If you're in Lewisham you must visit the Chef's Treat on Lewisham High Street. It doesn't have all the charms of a traditional greasy spoon insomuch as it isn't small and poky, it doesn't have rickety furniture on shared tables where you have to sit next to a 20 stone builder on his fifth lunch break that morning. But, it does have an excellent menu, including all the classics; breakfasts, burgers, roasts, various meals + chips, tea, good coffee and a dessert menu. The staff are very friendly, but will leave you alone if that is what you require, and the clientele is mixed - workmen, students, child and old person friendly. Decor is basic, clean and comfortable. Queues at peak times because it is very popular. Reasonable prices.
A good caff in Chelsea is the Chelsea Kitchen, SW3 4TZ.