Watering your Crop

[TOF]

I think you've hit on one of the perennial problems(excuse the pun!) Like you, I have a greenhouse full to bursting with plants growing on to plant out and this is just the first go around, I haven't started sowing the more tender summer veg yet and they require even more water.
From past experience, in cases of drought, I saved all the grey water (washing up water, etc) and used that to water the plants. Not ideal, but it's wet and it worked. One year I even diverted water from the washing machine straight to the garden and ran the machine late in the evening.
I have some barrels, but they wouldn't last long without replenishing, and to be honest, I would use them for people first and then recycle what I could for the plants. As to how much, while I was camping last year, I made myself manage on one gallon a day, for everything. So I think you could probably double that at home not including clothes washing.
I have a stream about 10mins walk away, and would use a couple of water carriers and my shopping trolley