Tries from Iestyn Harris, Barrie-Jon Mather, John Bentley and Stuart Spruce helped them to beat Tonga 20-0 in their opening game, and two tries from Denis Betts contributed the 28-10 defeat of South Africa later last night.
Last year's winners, New Zealand, who are Britain's opponents in the last of their pool matches today, were rather less impressive, beating Tonga 14-4 and France only 12-10.
Tony Tatupu, registered by Warrington for the coming season, scored a try for New Zealand against France after being cleared to play by the international board. His former club, the Auckland Warriors, are claiming that he is still contractually bound to them.
Britain also face France and Japan today and need to win only two of their three matches to be sure of a place in the semi-finals.
The side that beat them in the semi-finals last season, Papua New Guinea, are unlikely to be involved beyond the group stage this time, having lost to both the Cook Islands and Fiji on day one.
The tournament favourites and host side, Australia, won both their games, as did Western Samoa, making them the likely qualifiers from that pool.
Leeds are looking for a home-grown back-row forward to complete their squad after deciding to release the New Zealander Nathan Picchi.
Picchi fits within Leeds' overseas quota, but is being unloaded because of problems in obtaining enough work permits. Signed last season, he suffered a serious shoulder injury in his first match against Sheffield Eagles and has recently returned to action in Leeds' pre-season friendlies. Picchi is keen to stay in England and Leeds have said that they will charge no fee for him.
The French club, Villeneuve, have echoed a theme sounded this week by Celtic, by threatening to withdraw from their national competition and to apply to play in England.
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