You might find it easier (and cheaper) to find a local 'greasy spoon' as we call them. Basically a traditional café serving simple cooked (fried) food, not the new breed of fancy coffee shop cafe's. I wouldn't try asking for a Cappuccino or a Latte, it's tea or coffee, white or black... simple.
The key phrase to look for is 'all day breakfast'. These are where you tend to find the 'workers', so expect them to be rough and ready (not dangerous by the way, just simple with no glitz and glam). You will get a good traditional 'full English' for around £3-£5 depending on how big it is. Even the smallest towns usually have something like this. They can be harder to find in London as tend not to be in the tourist hotspots due to sky high rents.
Get a bacon butty (bacon sandwich, ask for well done, no fat) with red or brown (ketchup or brown sauce) and a mug of tea, sometimes called 'builders tea'. Chances are the tea will be included with the breakfast.