There's this that I posted awhile back from ATARN which shows and somewhat explains Ming Dynasty non-repeating crossbows with laminate prods. https://thearbalistguild.forumotion.com/t748-ming-dynasty-non-repeating-chinese-crossbow-build-it?highlight=ming
Read Stephen's explanations; it gives relative dimensions of each layer of lam, and a bunch of other good information.
There's not a lot written in English or even other European languages about loose laminate prods. The Chinese/Asians were masters of the concept but again little is in non-Asian languages. The Crossbow Building Wiki has some tech-talk: http://crossbow.wikia.com/wiki/Bow_design
You also get some ideas if you search Primitive Archer and Paleoplanet on "bundle bow".
Here's the very best discussion I can find on making a wooden loose laminate (they call it leaf spring) bow:
Basic idea is that you want the lams to 'free float' between the inner and outer lams. Only tie at the ends or a couple places around the outside of the stack; don't tie each lam in place. A tillering tree will let you see how the bow is bending.
Check local DIY shops or window covering shops for bamboo blind slats... Strips of bamboo flooring would also work.
My loose laminate prod is made from pieces of a 1/4" x 3/4" fiberglass chainlink fence Tension Bar.
Here in the US you can get spring steel strips of varying widths and thicknesses. Same should be true in England. Here, McMaster-Carr for example has a 10 ft length of 1" wide x 1/16" thick 1074/1075 spring steel for $44 that will be more than enough to build a 4-5 lam bow that will be the same as a solid 1/4" or 5/16" x 1" x 30" prod. Use a die grinder or dremel tool to cut pin nocks in the ends of the longest lam.