Cheap Flights - how do you get them?

You might find it cheaper to fly in two or three flights than one direct flight. Depending on where you want to go.

Cross Atlantic is a bit vague.

Where do you want to go Canada? US? South America?

I’ve never heard of cheaper flights for pensioners. If you book special assistance, you can have early boarding .
Try Sky Scanner for flights , they will list all flights from your departure airport , so saves looking at airline sites . Non direct flights are cheaper but obviously take longer and you have the stress of transiting through the airport to catch your next flight . I’ve done it several times.
For Europe I’ve found flights are cheaper on Tuesdays and Wednesdays. I haven’t tried that for long haul though .
You could look at Travel Zoo, Secret Escapes and Voyage Priv. These are more for a flight and hotel package but offer some good deals .