First, I hope you still have some power for reading the board despite the storm hitting Scotland!
I have two air purifier. The first is an "old" Bonnaire HEPA tower air purifier. It had a photo of a boxer on its package hence my decision to purchase it
I will end deaf soon with all the noise it makes, even at the lowest setting. When it is on I hear nothing else, not even planes despite being sometimes (rarely fortunately) on Heathrow flight path. The second one is a much smaller Vicks Hepa air purifier. Smaller but still too noisy even at the sleeping mode.
For me it certainly does help and after a few hours my allergies (eyes, nose) stop. Be careful when you change the filter as I had an "explosion" of dust when I opened the Bonnaire air cleaner the first time. I had dust all over me and also around me (up to a metre) in the bedroom resulting in a massive asthma attack because of it. Better to change it outside. It just tells you the amount of dust around London.
Try to get one with permanent filter as it will be much cheaper in the long term, and a silent one if possible. My Bonnaire uses two filters (about £15 each) and the small Vicks uses one filter (also about £15) and they need to be replaced every six months in theory.
I noticed the Filtrete FAP02 by 3M gets good reviews on amazon.co.uk. It seems it is decently silent. Unfortunately it uses a filter you need to replace every three months. Still, it looks it is more efficient than an equivalent hepa filter and if it fixes your allergies it is priceless.