As previous posters have pointed out, the A318 is perfectly capable of crossing the pond already (JFK-London City Airport). It has a stated range of 3,100nm. The existing A321 has a stated range of 3.200nm (not much different), and the A321neo has a stated range of 3,700nm.

Of course, the A318 that BA use is all-business class so presumably a lot less luggage, and fewer seats and people (but probably just as much booze!) than a mixed-cabin aircraft, but I would have thought the additional 600nm range of the A321neo would be sufficient to carry a full complement of passengers and luggage even without significant modifications. But then I'm neither a pilot nor an aeronautical engineer