Nothing at all. Just leave them in the soil for next year.

If it is Bearded Iris, and the leaves are yellowing some, I would cut off the yellow portions, just for the sake of neatness. That probably won't happen until later in the summer in the UK, though.

I trim my bearded Iris using an outward sloping cut from the centre towards the outer edges of the leaves. I end up with a peak in the centre. They end up about 4-6" tall and are neat and tidy for the rest of the year.

With Dutch Iris and Reticulata relatives, just let the leaves die down naturally, and cut them off--or gently pull them out--when they are completely brown. That will increase your bloom next year. I'll admit that I am not familiar enough with Siberian Iris, Japanese Iris, or Pacific Hybrid Iris, to know what to do with them.

As long as you do not have a boggy garden, especially in winter, they are fine to keep in garden.