If only it were as easy to differentiate on the basis of making money / not making money.
By far the majority of farms have at least one other income - wife works in an office, mart canteen, does cleaning, whatever, and/or hubby does contract work of some sort. And/or they do B&B or other 'diverse' activity on the farm.
We are very much in the minority hereabouts in that we do not have another income. But if we had a family, we would have to do something to make more money, we couldn't raise a family on what the farm makes. And frankly, although BH was comfortable enough on his own financially, the only reason I can get away with not having an income external to the farm is that I have a nice nest egg salted away from my rat race life. We wouldn't have been able to take advantage of some of the capital grant schemes without that, either, and the farm would by now be in desperate need of some investment.
In fact, thinking my way around the farms in our neighbourhood, I can only think of one where there is no other income and more than one person living off the income from the farm - and they are unmarried brothers, sharing the farmhouse, with nephews working the farm but also having other jobs. (A much bigger farm than ours, of course.)
A few years ago, there was some research done on farm incomes. There were very, very few where the profit exceeded the total subsidy income. Think about that for a minute... it means that almost every farm in the survey area (which certainly included England and Wales but I don't know whether it included Northern Ireland or Scotland) makes a loss without its subsidies. Now, most of the environmental subsidies are designed to compensate the farmer for farming in a less intensive, less profitable but more environmentally sensitive way, so that perhaps should be expected. It was still a rather chilling fact to me, though.