I can’t speak for your own place and conditions, but much of my food growing area has only 6 inches of soil. So I’d say that it all depends upon your climate conditions and your gardening methods. I grow almost all of our own food plus excess to trade, sell, and giveaway. For long rooted crops like carrots and daikon, I use container boxes.
It's never too late to start! I retired to homestead on the slopes of Mauna Loa, an active volcano. I relate snippets of my endeavor on my blog : www.kaufarmer.blogspot.com
What type of white rock? we have between 1ft and about 4ft of topsoil before chalk. (the closest test bore is just off our land (6ft off) and shows 30cm earth then 50m chalk.) it isn't a problem in fact it is an advantage as the chalk acts as a huge sponge water reservoir. The only time I really notice is when I want to put a post in and it's really hard and when the post is taken out it's white, or if the renters plough goes too deep and turns over a load of chalk/flint. As John says look at what's growing there naturally if that's doing fine then your plants will to, if it seems to be struggling then you will also struggle.
The only time I swear at it is when I try to pull parsnips. they have long enough roots to get into the chalk and then they cling on and I have to break the tips off to get them out!