Using random dates in July (27-31 July), Flybe advertise flights to/from LGW at �5.04 each way - with taxes, etc added on, this equates to �60-ish, assuming you don't check any bags. For the same dates, easyjet have flights from STN at �20-�23 each way (including taxes), again without bags. BA will do you flights from LHR at �38 each way, including bags.
Yes I know you said "flights" - the cheapest train fare London-Newcastle (booked 2-3m ahead) is �14 each way, with seats available on some very respectably timed services.