If you're in London and have a budget of £600 a month, the world is your oyster really, even with kids to feed you could get some cool stuff, there's endless fantastic producers in London. I don't get a veg box delivery service as there's no where to leave it in my flat and I can't be bothered to cart it home from work.
I am super lucky, I live in Covent Garden and work in Soho, so I buy my veg and stuff like brick lane bagels from the Bread Man on Berwick street Market, I get stuff like pandan leaves and fish sauce/sciracha etc from China Town, I get cheese from Neal's yard dairy and I get most of my meat delivered to my office from this guy who gets up at 3am to buy stuff from Smithfield market, I also like
http://www.thebutcheryltd.com/ Nathan has been a butcher at Ginger pig and barbecoa, I do also frequent the Ginger pig -
http://www.thegingerpig.co.uk/ and Allens of Mayfair, but they are expensive. We don't eat vast quantities (especially me) so if I do it has to be high quality (yes, I'm a meat-snob
)
We get our coffee from Monmouth or buy Square mile from Flat Cap.
I use Ocado to buy anything like laundry stuff and the grains, we buy a couple of processed things, mostly cereal and I will pop into Whole Foods in Piccadilly if I'm on that side of Soho. I'll also go to Lima for Italian Sausage or fresh Pasta.
It's just...a much different way of shopping to what I'd do in the US, which is probably hit up HEB or Whole Foods, for what it's worth whenever I go into a HEB or Trader Joes in the US I always seem to end up spending a fortune and am surprised by the cost.
Also I appreciate that not many people have the time/budget/energy to do all of this, I can because it takes 10 seconds to get to Berwick street or to Lima, or five minutes to get to the Ginger pig and I'm fortunate enough financially to be able to prioritise this aspect of my life.
Smithfield market prices, in case you're interested -
T-bone steak - £19.00 per kg
fillet steak - £26.00 per kg
Dry aged ribeye steak - £25.00 per kg
Gressingham duck - £8.00 per kg
pig cheeks - £7.50 per kg
pork belly - £7.50 per kg
corn fed chicken - £6.50 each
leg of lamb - £10.00 per kg
shoulder of lamb - £9.50 per kg