Gosh, five allotments is a big area, and straw is a possible source of organic matter once composted to become reasonably dark and crumbly. Mushroom compost is mostly straw for example. But tcomposting it takes time and needs space, maybe use part of one allotment for doing it.
The problem with applying fresh straw mulches in our damp climate is slugs hiding and breeding underneath it. I tried hay and straw mulches once in 1983 and quickly realised their limitations! But composted straw is good and if you can find a little manure and green matter to add, that will improve the speed of process and quality of your result.