Tricky but not impossible.
The Nut Shop Leeds Market offers a wide range of nuts and dried fruit, even loose sprinkles for cakes. By weight. Details HERE
If you cannot get to Leeds you can try
Wholefood Market a supermarket chain
Weigh & Save shops a UK franchise
And other loose food outlets as listed below
Loose Food A to Z
Find out if a shop near you sells bulk food loose. This is stuff that that normally comes plastic packaged ie rice, pasta and salt. And yes these shops do exist in the U.K. There’s just not many of them.
Heres alist of towns with shops selling loose food.
While these shops provide bags and they are almost always plastic ones. You will need to take your own plastic-free /reusable bags.