Hiya.....
Just had a look on the net and NYC to London is approx 3050 nm.... I'll dig out the FCOM 3 to look at the fuel required for 2800 nm cruise to landing and add 160 miles for the climb to cruise altitude. This is not accurate but hopefully will suffice for your question.
12300 kg burn in the cruise/landing + 1800 kg for the climb, to FL370.
So your trip fuel alone is 14100 kg.
The 319 is capable of carrying 18700 kg. You need 17100 kg for this "trip" with IFR reserves. IFR reserves are.....alternate fuel, say 1000 kg (depends on where the diversion airport is), contingency 5% of the trip, 705 kg....taxi fuel...final reserve fuel...approx 1000kg. So approx 3000 kg IFR reserves on top of the 14100 kg trip. Thats 17100 kg in total.
Using average weights for this example of 85 kg per pax thats 10500 kg (assuming each pax has the standard 13 kg bag in the hold).
The A319, well ours at easyjet are about 41000 kg dry operating weight, thats with 156 seats, so with a different seating capacity that would be lower. For the sake of arguement lets go with 40,000 kg for simplicity. Add the 17100 kg of fuel and the pax weight and we end up with a grand total of 67600 kg.
The A319 max take off weight is 68000 kg. So the short answer is YES !!
Phew - right I'm off to bed, on an early tomorrow.
Cheers