I bought one over ten years ago from Amcor for my asthmatic husband, and we are very happy with it. Still running 24/7. It has an ioniser (not convinced that ionisers do very much) and a HEPA filter which filters out tiny particles. They also supplied a washable filter, which is much cheaper and reusable, although I have hoovered the hepa filter several times and then reused it too. It has two speeds, one for constant use, one to clean a room quickly. The faster mode is slightly less quiet, the slow mode is very quiet. I notice the difference with or without the machine on. We have it in the bedroom. Hubby is not bad enough to need the whole house doing.
Unfortunately they are not selling that model anymore, but there are similar machines around, based on the principle of a slow blower in reverse, which is sucking air in and cleaning it by running through a filter of some sort.
There are much more expensive models available too for really serious allergy sufferers. Filterless models too. The first type costs around 50 pounds the second several hundred.