The options are as follows.
Train to Exeter from London (or Reading if coming direct from Heathrow) Bus to Bude then another to Tintagel.
or
Train to Bodmin Parkway from London, then either taxi to Tintagel,about £20 or bus to Wadebridge then another to Tintagel.
See www.travelineSW.com for times etc

There are coaches to Exeter and Bodmin from London with National Express.
If you can drive it is much better as public transport takes forever!