That may well be as cheap as you'll get, it's a fairly long segment at high season. July and August fares are always high. Air Passenger Duty is also a large proportion of the fare these days, and cannot be discounted. You may be lucky and get a decent fare from a consolidator site like Kayak. Skyscanner and Expedia may also have decent prices. I've found uniquely low fares on Kayak, just may have been luck. Booking direct with your chosen airline is often the best.
You may also consider a change in Europe if price is important. I did LHR-MAD-ORD for £1100 in business class a couple of years ago. You can connect through Schiphol or Charles De Gaulle from Birmingham and other smaller airports (KLM/AF/others) and may be more convenient than getting to LHR or MAN. Icelandair from Heathrow via Reykjavik has a reputation for being great value, but a poor in flight experience.
Go for a European airline, as the American carriers can be low frills. Also the current exchange rate will penalise you if booking a flight priced originally in dollars. Virgin and BA are usually well matched on price, and BA is probably a marginally better in flight experience these days. Both are much better than AA or UA or the other Americans.
Word of advice about ORD. It's rated quite highly in general but I've found immigration and security are extremely inefficient. Allow plenty of time.
And Chicago will be very hot and humid in July, be prepared!