One possible option might be:
Luton Airport Parkway - London Thameslink Off-Peak Day Single £13.90
London Terminals - Southend Central Anytime Day Single £11.40
Total cost £25.30. This ticket combination isn't valid on London Underground, so you would need to walk between London Bridge and Fenchurch Street stations. Not particularly far, but if you had luggage you might not want to do that.
An option valid on the Underground could be:
Luton Airport Parkway - London Zones 1-6 Off-Peak Day Travelcard £20.50
Boundary Zone 6 - Southend Central or Southend Victoria Anytime Day Single £8.00
Total cost £28.50