Stockton is sitting on a score of 42.7 on Westwood Poser, narrowly overtaking previous leader Mary King.
British riders dominate the top ten, with Irish riders next.
King is second on Imperial Cavalier (44) and third on Fernhill Urco (45.2), ahead of Oliver Townend (Jackson D'allez), Pippa Funnell (Blue Horizon), Piggy French (What A Performance), and Townend and Golden Hue.
Ireland's Ciaran Glynn and Killossery Kruisita are eighth on 49, while last year's winner, Captain Geoff Curran, lies in ninth on 47.9 penalties with The Jump Jet. Curran's winning horse from 2008, the Minister for Defence's Kilkishen, accumulated 55.4 penalties in dressage and now lies in 26th place overall.
Sharing 10th equal place is New Zealand's Mark Todd and Land Vision (50 penalties), and two Irish riders, Declan Cullen and Glenhill Gold, and Michael Ryan and Master Mexico.
Of the rest of the Kiwi contingent, Caroline Powell and Mac Macdonald share 19th place with Australia's Clayton Fredericks and Mr Miller 2, on 52.3 penalties.
Powell's second mount, Apapa, shares 27th place with Todd and Gandalf, with 56.2.
The cross country phase of the World Cup qualifier takes place today, with showjumping deciding the eventual winner tomorrow.