Allcock, who trailed 8-3 after seven ends, strung together a sequence of 11 shots over the next five ends to establish a 14-8 lead and he maintained that advantage over the next four ends to lead 18- 12. He then produced a powerful finish with nine shots on the next five ends.
Scotland's Richard Corsie, a gold medallist in the pairs, also produced a strong finish to beat Thailand's Sujit Sopon 25-14 after leading 16-14. However, Corsie's success was short-lived. In the second round he opened up a 22-12 lead over Bill Moseley, but the South African recovered to win 25-23.
The surprise result of the first round was the defeat of Ireland's Stevie Adamson, who lost 25-23 to Singapore's Chai Hon Yoong. Adamson had finished second, with Sammy Allen, to Scotland in the pairs event on Saturday. Chai was unable to maintain his form, though. In the second round he was beaten 25-4 by Mark McMahon, of Hong Kong.
New Zealand's Peter Bellis, the world champion in 1984, beat Joe Akaruru 25-14.
In the fours, the England rink of John Ottaway, Roy Cutts, Andy Thomson and John Bell recovered from a 14-10 deficit to beat Cook Islands 20-16. Scotland had the biggest win of the day, 54-10 over Thailand.Reuse content