Try the national rail or First Capital Connect websites - there is one train that goes from Luton - Luton Airport Parkway - London - Gatwick, so you wouldn't need to change.
Edit - I think the website you need is called train2plane.com or something similar
Answers & Comments
Verified answer
Try the national rail or First Capital Connect websites - there is one train that goes from Luton - Luton Airport Parkway - London - Gatwick, so you wouldn't need to change.
Edit - I think the website you need is called train2plane.com or something similar