What do you have in the way of tools? How big is this patch? If it isn't too large you could use hand shears and cut back to 6". Power hedging shears would be best for your body. There are even brush cutting mowers you could rent if the area is large. Leave the clippings. They will cover the bare spots and stop any weed seed from germinating.
As Bamboo warned, right now timing is critical. If you chop the ivy back too 'late' the ivy will have just enough time to put on new tender growth and when winter hits the cold will fry the new leaves. I doubt it will kill the ivy but it will look awful. Depending on your zone and winter conditions, I would wait until early spring to cut down. If where you live has another 2 or 3 months before the soil freezes go ahead and get 'er done now. Leave the clippings or at least 'blow' them off the top of your ivy plants and down into the vines/soil. They will inhibit germination of 'other weed' seeds and decompose to improve the soil. Do NOT fertilize until spring. Fertilizing will produce even more tender vegetative growth for the winter to kill.
There are two types of foliage on Hedera helix. The young plant growth you are probably used to and then once a plant matures you'll see the mature plant leaves which are very different. You'll start seeing the reproductive growth as well. Because this plant is highly invasive, if you want to continue to use this as a ground cover, it is only right to continue a maintenance program to cut your ivy back and reduce flowering and seed. Ivy is even better at reproducing from every little chunk of stem and or root (vegetative reproduction). Cutting or 'mowing' your ivy is completely necessary. Necessary as well is limiting where your ivy is ALLOWED to grow.
All of your trees, shrubs should have a 'circle' of bare ground (mulched) so the ivy is not able to grow up your trees. You will have to maintain these transition areas by pulling up any ivy you see. Keep it off the home as well. All other plants and/or your lawn should have a zone between the ivy and the plants. You could use that thin plastic barrier stuff sold in most hardware and nurseries, bury it 6" deep all along the borders where you do not want the ivy to cross. That will help somewhat. Twice per year, I'd chop your 'crop' to 6". Early spring and Early fall/late summer.
The proper formulation of fertilizer will be a major factor in keeping your ivy from seeding. A high nitrogen formulation such as 10-4-6 or 20-7-8 where the first number, percentage of Nitrogen in the bag, is quite a bit higher than the second and third number (phosphorus and potassium). This will help to inhibit any reproductive growth (flowers and seeds). Once per year a light, high Nitrogen, fertilization is plenty!
If you've got too much vegetative growth after a mowing to leave, go ahead and dispose of in those large black plastic bags. Make sure you keep those bags of vine material labeled. To dispose in the normal garbage dump is irresponsible. Each little chunk can easily start a new smothering crop somewhere else. If you could find CLEAR plastic bags, fill with your ivy debris, and leave in the sun to 'cook'. After 'cooking' for a few months, take to a dump that handles 'clean green' grass clippings (here in the states a dump has to have a special license to handle 'clean green') and they should know how to properly compost garden debris. Make sure they know you've got bags of vine clippings that you have tried to 'cook'. They will be impressed!
One other thing about this ivy, especially as it gets higher are RATS. This is a wonderful place for rats to hunker down in and travel unnoticed. When you keep this ivy crop of yours cut down twice per year you will not have to worry so much about creating a great rat population. Rats are limited in population by the King Daddy rat who kicks his progeny out as soon as they can be on their own. On your property will be his harem and maybe a successor or two living along with the King but your neighbors will get the young that will make their own kingdoms. All those sewers and caves with zillions of rats are just the 'nightclubs'...
Sure you don't want to have a lawn or a nice graveled forest floor??