I recommend the flight search site matrix.itasoftware.com, which is nice because it offers a ton of search options, and only shows you information, they don't sell you flights, so you can trust them. There are a number of hidden advanced options, one of which is
/ -redeye to rule out redeye flights. If you are flexible with your origin and destination, you can enter multiple airports (including the "generic" city codes for some cities, such as
NYC for any New York City airport,
LON for any London airport, etc.)
In your case, from the comments, I take it that you are not limited to only LHR, and perhaps not even NYC, so in the screen shot below I did a search for departure from any of New York City, Philadelphia, Washington, or Boston, and arriving at any of London, Amsterdam, Brussels, Copenhagen, or Dublin (obviously, change the search to suit your desires). I also indicated no redeyes, and requested a 30-day search for the lowest round-trip economy fare for a two to eight day stay (again, change to suit).
See the three screen shots to see what I mean: First, the search query:
Next, the search results, which show that the least expensive options for the given criteria is a 7- or 8-night stay departing on June 11 for $859:
Finally, the flight info screen (from clicking the price on the search results screen) which shows a number of options for day flights from various East Coast airports to various European airports at a range of prices:
Note that the flight info screen shot is truncated to fit; there are many more flights available; I am only trying to show how to do a search, not provide the exact answer for your situation.