That is a small garden to have 20 conifer stumps in it, was the whole thing basically covered in conifers? Sorry to be a wet blanket but there is no way you can grow veg in a garden full of conifer stumps. Even if you created raised beds as the stamps rotted you would have problems. You either need to dig them out or accept that you can't grow veg - doubt you'll be able to grown anything else either.

Is the photo taken morning or evening? there seems to be quite a shady strip near the fence where veg would not give the best results anyway, I have left a conifer stump a lot bigger than those and planted round it successfully.. As digging them out isn't an option perhaps you could leave a strip two or three feet wide from the fence and grow your veg in front. You'll likely encounter smaller roots and just take them out as and when you can. The stumps will rot down on their own eventually.
Keep the things that need deep digging eg beans and potatoes well over to the other side and remember to add lots of good compost this autumn.

Stera is right in that if you grow your veg 3 foot, or more, away from the stumps then that could work. Question is how big is your garden and how much of it are you wanting to turn over to veg? Unfortunately veg are a lot of hard work to grow however you do it.

Yes, lots of stumps. it was originally the barrier between the two gardens. I don't want to grow lots of veg, just start a few little veg patches for the kids mainly. So we can enjoy growing something and then cooking it after.

This is my first garden and it had so many flower beds and we have found it so hard to maintain. So we plan on making some raised beds for veg patches near the fence. I am just not sure what will grow there if the stumps are left. If we dig them out are the chances of growing successfully higher?? My husband is not keen on gardening and it's hard to find the time to dig stumps out between work and entertaining the kids. Maybe I have no option but to dig them out if I really want to grow.

The garden is north facing ? But We do get a lot of sunshine in the garden along the fence side until about 7pm in the summer.

The soil around the roots of the stumps is now as hard as concrete. You will need a sharp spade, a pickaxe, a long crowbar, patience and finally plenty of muscle and stamina.
Best to make a small raised bed over the stumps for your children to plant some veggies in and have them tend to it. It will be fun for them for a little while and when they finally turn their attention to something else you take over....you know...the same thing when they get a puppy.

Think easy to grow veg then like salad leaves, peas, radishes, spring onions, chives, possibly tomatoes. I wouldn't suggest root crops a these need a lot more attention. Buy tomato plants rather than starting from seed, you can also buy brassica plants but I'd suggest you avoid cauliflowers. Good luck hope it works for you.

Those conifers weren't very big at all. You'll have to remove the stumps if you want to make use of that strip. I've ripped out bigger stumps than those with a pair of lopers and my bare hands. I felt like Godzilla, lol. Maybe you can hire somebody?

Thanks everyone. We have admitted defeat and began digging them out. 2 are out already. Determined to grow something there. Hopefully the hard work pays off.

It will E1timer...

Sorry I always talk too much and get a bit carried away, But....
Also though you were advised to avoid the cabbage family you would still have time to put in a few winter varieties which you can get as small plants now. No need to wait until the whole row is cleared, but it you add some good compost to the bit you've done you'd have room for a few and it might get the kids interested and give you some free veg later. Its a bit late to plant anything much else except a few lettuce plants until next year.
If you like rhubarb I think that would do well there, though you do have to wait a couple of years before you can pull any. You could also grow red and black currants in that spot.

How old are the kids? Best not to try too hard with them - if you are interested they probably will be too especially if they have their own little trowel and watering can.. There are easy flower seeds for next year that might interest them.