Ludlam impressed as a replacement in the opening two matches but he will now get the nod in the seven shirt, coming in for the injured Sam Underhill.
Courtney Lawes once again skippers the side from six, while Tommy Freeman, who made his Test debut in the 25-17 win in Brisbane last weekend, keeps his place on the wing.
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“We go into this Test with a strong squad of 23. It’s a young, inexperienced but together group who have developed well throughout this series.
“We want to play with purpose and energy to win the series and an historic Test match at the Sydney Cricket Ground.”
England team to play Australia: 15. Freddie Steward (Leicester Tigers, 12 caps); 14. Jack Nowell (Exeter Chiefs, 41 caps), 13. Guy Porter (Leicester Tigers, 1 cap), 12. Owen Farrell (Saracens, 96 caps), 11. Tommy Freeman (Saints, 1 cap); 10. Marcus Smith (Harlequins, 12 caps), 9. Danny Care (Harlequins, 86 caps); 1. Ellis Genge (Bristol Bears, 38 caps), 2. Jamie George (Saracens, 68 caps), 3. Will Stuart (Bath Rugby, 22 caps); 4. Ollie Chessum (Leicester Tigers, 4 caps), 5. Jonny Hill (Sale Sharks, 14 caps); 6. Courtney Lawes (capt) (Saints, 95 caps), 7. Lewis Ludlam (Saints, 13 caps), 8. Billy Vunipola (Saracens, 63 caps)
Replacements: 16. Luke Cowan-Dickie (Exeter Chiefs, 36 caps), 17. Mako Vunipola (Saracens, 69 caps), 18. Joe Heyes (Leicester Tigers, 4 caps), 19. Nick Isiekwe (Saracens, 7 caps), 20. Jack Willis (Wasps, 3 caps), 21. Jack van Poortvliet (Leicester Tigers, 2 caps), 22. Will Joseph (London Irish, 1 cap), 23. Henry Arundell (London Irish, 2 caps)