We have a basement kitchen which was dug out about 25 years ago and wasn't insulated. Behind the kitchen units there is a void up to the retaining wall on one side and an external wall on the other. I'd like to add some insulation but I'm limited in what I can do given the size of the space and the gaps into it. I've attached photos of the void
What's the best thing I could install?
Void between units & retaining wall
Void between units & external wall
It's hard to tell for sure, but it looks like the smallest depth is ~2ft from the brick wall to the back side of the wooden wall.
Since you're interested in maximum R-value, filling a 2' gap with spray foam will give you great R-value! Won't be cheap but it'll be warm. Since it's a fairly narrow gap, that would probably also be the easiest to install since it would only require sticking a spray gun and an arm into the gap and wouldn't require getting a body and/or fixed size materials into the gap.
Of course, if the gap is bigger than that, it opens up other options.
If you have less than infinite money to waste on this project, 4-6" of rigid foam is probably the point where the payoff (from more R-value) doesn't meet the expense of buying more insulation. Assuming the walls are indeed below grade (since we seem to be looking below the countertop level of a basement kitchen) likely the thinner end of that, as it won't be as cold outside a buried wall as it is aboveground in winter.
It would appear that you can cut long sheets to fit the height and shove one into the corner, apply foam adhesive or spray foam to the end of another sheet cut to fit on the other side, and shove it in so the two join at the corner without having to crawl in there from the wider side.
You could also choose a rigid rockwool product which will be considerably safer in a fire, though it may also cost quite a bit more.
