I think the local tip will be next You are probably right. Ours are already closed.
Excellent time to start compost! Don't put in troublesome perennial weed - basically anything with fat fleshy roots - take the leaves off and add to the heap, but bag up the roots for later disposal (or leave them out in the sun until they're well and truly dried up and dead)
Stand the bin on soil, so that worms and microorganisms can find their way in.
Once you've got a solid 6inches of weeds at the bottom, scatter about an inch of soil on top before putting more weeds in (unless you've already got clods of soil on the roots of the weeds).
You can also add vegetable peelings from the kitchen, cardboard and paper that isn't heavily printed - as a rule of thumb, if it's used to wrap food, the ink will be nothing to worry about. Also grass cuttings. But don't have too thick a layer of any one thing.
You'll find it compacts as it rots, so the heap will be full to the top one day, but a week later you can get some more in. When you really can't get any more in, empty it all out, and hopefully the bottom layer will be ready for use, as compost if it's really good, or as mulch if it's not quite rotted. Put all the unrotted stuff back in, and you'll now have a bit more space to add stuff.