I've been to Europe three times since 2006 (twice to England, once to Scandinavia), and the price from Minneapolis was above $1000 in all cases.

Have you tried different dates (change them a day or two) or different gateway cities or different airlines?

and would be really fun.

Otherwise, you'd probably get to sample an NHS emergency ward.

The train is another option once you're on the British mainland. A BritRail pass can be a real money saver, because rail fares in the UK are structured like plane fares (thank you, privatization! ) and the price of a ticket can vary tremendously depending on how far in advance you buy it.

Unfortunately I have to meet someone at Heathrow on the morning of Oct. 20th and due to work I can not leave early.

I am shocked time and time again looking at these prices!
What airports in London have you tried in your fare search? Try Birmingham (sometimes I used to see a difference with the smaller ones , but havent used airoplanes in years now due to the prices)
Maybe have a look at Stansted too. Try and avoid weekends if possible, I remember that from a Friday to a Thursday would be a significant change!

But I did find a flight for $929 flying out of the midwest on Air Canada of all things. I checked farecaster.com and they advised to buy.