American Airlines, British Airways, and Finnair have round-trip flights from Dallas (DFW) to London, Dublin, Paris, Madrid, Helsinki, or Frankfurt (LHR, DUB, CDG, MAD, HEL, FRA) for $416-$577, NONSTOP. Flights October to May. Extended weekends available.
London is the most expensive fare in this group at $577.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.