Fabio Capello's men, looking for their first win at South Africa 2010, struggled to create chances against their African opponents and failed to grant their manager a happy 64th birthday.
After qualifying for the finals so convincingly, Capello himself will expect scrutiny over sticking with a 4-4-2 formation and keeping faith with striker Emile Heskey at Green Point Stadium.
The big decision prior to the game was whether to pick Robert Green in goal following his error against USA last week in the Group C opener.
After assessing the goalkeeper's mentality, the England manager opted for 39-year-old David James, who was making his debut at the finals of the tournament.
Algeria boss Rabah Saadane also changed his goalkeeper after Faouzi Chaouchi's mistake in the defeat to Slovenia, although the 25-year-old also suffered a knee problem before the game.
His replacement, Rais M Bolhi, made a nervous start when Steven Gerrard's harmless cross almost drifted in, but he was not troubled regularly as England failed to impose themselves on the match.
Frank Lampard, seizing onto a clearance by defender Rafik Halliche, did force M Bolhi into a decent save with a drive. But England's other efforts from Wayne Rooney and Gareth Barry went straight at the goalkeeper.
Capello was furious on the touchline, especially as his side could have conceded the opener.
James looked unconvincing punching an early corner, then he was forced to claim the ball after Jamie Carragher, replacing injured Ledley King in the starting line-up, missed a cross completely.
Hassan Yebda also headed on target, although it was straight at James, while Karim Ziani shot wide when Algeria launched a counter-attack.
It was a poor opening half from Capello's men but the Italian did not make changes at the break, and it did not get better for them immediately after the restart.
Just before the hour mark Carragher was booked for a foul on Yebda which meant he would miss the final group game, against Slovenia.
Capello eventually brought on Shaun Wright-Phillips and Jermain Defoe and England started to look more dangerous, although they failed to grab the winner and had to settle for back-to-back draws.
England (4-1-3-2): James; Johnson, Carragher, Terry, A Cole; Barry (Crouch 84); Lennon (Wright-Phillips 63) , Lampard, Gerrard; Rooney, Heskey (Defoe 74).
Subs (not used): Green, Hart, Dawson, Upson, Warnock, Milner, Carrick, J Cole.
Algeria (4-5-1): M Bolhi; Kadir, Bougherra, Halliche, Belhadj; Boudebouz (Abdoun 74), Yahia, Lacen, Ziani (Guedioura 80), Yebda (Mesbah 88); Matmour.
Subs (not used): Gaouaoui, Chaouchi, Bellaid, Laifaoui, Medjani, Mansouri, Saifi, Djebbour.