That right, lb... you will not go through immigration at Heathrow since you will have cleared immigration in Dublin. You will not get a stamp showing that you entered the UK, which makes it difficult (but not impossible) to show that you have lived there for two years when it comes to applying for your ILR. If you do enter through Dublin, make sure you keep your ticket stubs and any bills that you get soon upon your arrival to prove your residency. The other option is to take a little trip to Mainland Europe within a few weeks of your arrival (even through the Channel Tunnel to France) and then you will be stamped upon your return to the UK.
The Delta flight that Chary refers to is available on Orbitz and Cheap Tickets.
I also found a flight on Vayama for $575, for travel on Aug 21. All it will tell you is that it is on a Star Alliance flight (which is United, Lufthansa, Air Canada and a few others), and they only give you windows of time that the flight departs and lands, but they allow you to cancel within an hour of booking if you dont like the flight given.