India's morale-sapping second Test humiliation against England has triggered a desperate wave of soul-searching back home with some former players questioning spinner Harbhajan Singh's place in the side and the appointment of coach Duncan Fletcher.

India arrived in England as the top-ranked Test team and still basking in the glory of their 50-over World Cup victory on home soil in April, but the tourists have been comprehensively outplayed in the first two contests of the four-match series.

Mahendra Singh Dhoni's men lost by 196 runs at Lord's last week and were battered by 319 runs within four days at Trent Bridge on Monday, putting England on course to claim the top ranking if they complete a series win by a two-victory margin.

To arrest the slide, India should axe the off-colour Harbhajan, former captain Bishan Singh Bedi told the Times of India newspaper, which also ran a front page opinion piece headlined: 'This team does not deserve to be no. 1 Test side in the world' on Tuesday.

"There's no point discussing his lack of flight or lack of spin or his action because we have been doing that for years," Bedi said of the off-spinner who conceded 218 runs for a single wicket at Lord's.

Nursing an abdominal strain, Harbhajan fared little better at Trent Bridge, sending down just 13.4 overs that cost him 69 runs for the wicket of Stuart Broad.

"He lacks guile, and that's a great handicap for a spinner. The right areas to bowl lie not on the 22 yards but in between your ears, in the mind," said Bedi, whose craft and cunning earned him 266 wickets from 67 Tests he played from 1966-1979.

The former left-arm spinner said Harbhajan should return to domestic cricket to rediscover himself and India should include either leg-spinner Amit Mishra or pace bowler in Munaf Patel for the third Test starting in Birmingham on Aug. 10.

"I think it's a toss-up between Munaf and Mishra now because Harbhajan has played enough on the weight of reputation alone. He clearly lacks the confidence. A stint in domestic cricket would do him good.

"As a senior player, if you're not feeling up to it, you should put your hand up and say so. I don't think he deserves such a long rope anymore."

Former opener Angshuman Gaekwad also backs the inclusion of Mishra for Harbhajan in the third Test.

"Mental pressure leads to technical problems too. Harbhajan is not bowling like an off-spinner. He has virtually no follow-through and no transfer of weight.

"He is bowling with too much effort and trying to save himself from getting hit. I believe it's better for the team if Amit Mishra is drafted in."

The back-to-back defeats made former batsman-wicketkeeper Farokh Engineer wonder if Fletcher was the right man to coach India.

"What are these highly-paid coaches doing? The results are not showing. What is Fletcher doing? Just because (predecessor) Gary Kirsten recommends him, is that sufficient to get the job?" Engineer asked in the Hindustan Times newspaper.