I think that the only way to reach the USA is from the Azores. Ryanair's Boeing 738 range would not be enough to reach the USA from London in safety. From Boeing's website we know that the maximum range is 3060 nm and from STN to JFK we have 3016 nm. From Lages (TER) in Azores to JFK it's only 2139 nm. The longest FR route at the moment is from AGP to TMP and has 1824 nm.
Europe to Lajes would work, however Lajes to US is not possible with the 737 because of missing ETOPS approval.
It is simply not allowed to fly over such a large pond without good ("suitable") alternate airports on the way!