The chances are, when you first take on an allotment, you will be faced with a chest-high sea of weeds.
This can seem overwhelming at first, but there are many ways to tackle the problem and bring your plot under control, and if you are prepared to put in the time and effort, it can be done organically. The key is to be systematic about it, starting at the front and working back, rather than trying to tackle isolated islands within the plot, which are quickly overgrown.
Using a scythe, shears or strimmer, cut down the tall weed growth. If there are many dried seed-heads it is best to pile this up and burn it, otherwise this can be left to compost where it falls, or added to a compost heap.
Cutting down the top growth won't kill the weeds - at least not the perennials. Using carpet, cardboard, paper or woven plastic mulch (the committee sells Mipex landscaping fabric at cost price), cover your plot for a season to cut out the light. This will kill 90% of the weeds.
Before you lay a mulch, remove any rubbish. This helps it fit more 'snugly', and makes it less likely to fly away in the wind.
When laying it down, always secure it properly. The best way to do this with Mipex is to cut a slit in the ground with your spade, and tuck it in along the edges. Failing this, you can peg it, and/or weigh it down with something really heavy (think concrete blocks or scaffold bars). Otherwise the winter gales will rip it up and leave it flapping over your neighbour's plot.
Never leave a plastic or carpet mulch two seasons in a row without lifting, scraping it clean, and re-laying. Mulching is not a permanent solution to keeping a piece of land clear, and if you leave it for much longer than a year then mud accumulates and weeds will start to grow into it. Once the couch grass has started to grow through carpet or Mipex, it becomes worse than useless and is a real pain to dispose of.
After six to nine months, the mulch will have killed most of the weeds for you. Lift it off and dig the ground underneath. (paper or cardboard mulches can be dug in or composted) As you are ready to cultivate a new section, you can just move the mulch along.
You are likely to find great white brittle coils of bindweed just under the mulch, and the long, fibrous roots of couch grass under the soil. Carefully remove all traces of these roots as you dig, or the weeds will be back before you know it. I have heard dire warnings about composting weed roots, but so long as they are properly dried out, this should not be a problem.
Clearing a plot of weeds is not a one-off job - it is ongoing. If weeds have been allowed to seed themselves, there will be a 'seed-bank' in the soil which can last for decades. New seeds are also continually blowing in on the wind. Although the procedure above will get rid of most of your most troublesome perennial weeds, regular weeding throughout the year is still needed to keep your plot clear and prevent your crops from being swamped.