Too eager on buying flight ticket?

Have you tried Icelandair? We have done a one way Paris-New York in June (with an overnight in Reykjavik) for $500 each. You could play around with the cities and see what you come up with.
Another airline we use that frequently has sales is SAS.

http://www.skyscanner.net/transport/flights/uk/nyca/150710/cheapest-flights-from-united-kingdom-to-new-york-in-july-2015.html?rtn=0

Do a search using Skyscanner.net from the US & you should have prices in US Dollars.

We did that too! We booked one way and then it took hours and hours and days to find lower fare return tickets. We looked in the middle of the night when prices are really low and watched them go up in price, literally by the minute. So my suggestion is to keep trying. I was told to empty my cache and then the price would come in lower as the algorithm would not recognize me as a previous search. ( I didn't do that because I did not want to delete my search history.) We bought $375.00 tickets to fly from San Francisco (flying out of Oakland) to Copenhagen! Then $73.00 each to fly from there to Rome on Easy Jet. For the return flights from Rome to Oakland we finally found the great price of $395.00 each. These are on Norwegian Air Shuttle. We used at least 2 flight search sites: Cheap0air and actually, any others that popped up. We saved a lot of money and we do acknowledge these are budget airlines. Worth it to us. Good luck.

Affordable one-way fares are the exception, not the rule, but I'm encouraged to hear that others have made it work.

Also try Norwegian air. The don't show up search engines like dohop or orbitz

Looking at Norwegian is a good idea. Right now they have one ways from London to JFK on your date (July 17) for $514. I know that's a bit more than your desired <$450 but finding a one-way from anywhere to JFK in July for that price is going to be very difficult if not impossible.

So many flights for the Summer are over $1500 round trip. I use MatrixITAsoftware.com to research flights.

You can sign into Norwegian.com. Many of their flights are limited--not offered every day. It and Turkish Airlines are about the cheapest of the cheap airlines.