My first port of call when looking for cheap flights is:
www.skyscanner.net<BR><BR>

Here's a couple of options you could look at:
Denver - New York (JFK)
Wednesday 13 June 12:55am - 6:33am
Jet Blue
US$89.40
New York (JFK) - London Heathrow
Wednesday 13 June 6:45pm - 10:05am (14 June)
Aer Lingus
flight goes via Shannon
US$333.66
TOTAL $423.06
************
Denver - New York (JFK)
Monday 11 June 1255am - 6:33am
Jet Blue
US$169.40
New York (JFK) - London Heathrow
Monday 11 June 6:45pm - 10:05am (12 June)
Aer Lingus
flight goes via Shannon
US$387.66
TOTAL: $557.06
************
Both options do give you about 12 hours in New York but when you are taking 2 separate flights rather than one connecting one I always think it's safer to give yourself as much time as possible to allow for delays etc.
In the past I've booked with both Aer Lingus and Jet Blue with a New Zealand credit card and have had no problems.