You often get much cheaper flights to North America from Dublin because of the heavy ($200 USD equivalent) departure tax out of London.
From Dublin to London, check Kayak or Google Flights. Remember a couple of things:
(1) The discount airlines can be very restrictive with baggage policies. Make sure you clearly understand what is and is not included in your ticket. EasyJet and I believe now Ryanair allow you one piece of baggage (no separate personal item) TOTAL. You can get around this by buying priority boarding (usually only a few pounds/Euros), but if you don’t, you’ll be hit with a 40 Euro/pound fee.
(2) Be mindful of what airport you fly into and out of. Luton is very far from London and requires a bus to rail connection. (It is also the nastiest airport I’ve seen in Europe — looks like a temporary structure.). Stansted is also far from London, an hour or more by train to most places. And Southend-on-Sea..... for awhile, I thought it was made up, but it does exist; again, very far from London. It’s worth a premium to fly into Heathrow, City, or (depending on where you’re going) Gatwick.