London (AP): England was all out in its second innings for 478, for a lead of 344 over New Zealand less than an hour into the final morning Monday of the first test.
New Zealand was set almost 80 overs to score 345 to win, a record at Lord's.
England captain Alastair Cook added only nine more to his overnight total before he was dismissed by fast bowler Trent Boult for 162. He was done in by a faint inside edge, bringing an end to just over nine hours at the crease.
England resumed on 429-6, and lasted only 11 overs, adding 49 runs. All four wickets went to Boult, who took 4-9 in 17 balls for a 5-for.
Broad was bowled for 10, Moeen Ali was leg before for 43, and James Anderson lost his off stump before scoring, leaving Mark Wood on 4 not out.
New Zealand will make history if it chases down 345. The highest winning chase at Lord's was in 1984 by West Indies, 344-1.
New Zealand's highest chase achieved was 324 in 1994 against Pakistan in Christchurch.