The victims of two disgraced doctors lost a battle in the High Court yesterday for full public inquiries into their cases.

Patricia Howard and Sheila Wright-Hogeland, who waived their right to anonymity, had called for open investigations of Dr Clifford Ayling, a GP who sexually assaulted patients, and Richard Neale, a surgeon who botched operations.

They claimed that the decision by Alan Milburn, the Secretary of State for Health, not to allow the press and public to attend formal investigations into the two doctors' "malign activities" was "irrational" and in breach of human rights laws. Mr Milburn insisted private inquiries would be fairer, faster and more cost-effective.

Yesterday, his decision was upheld when Mr Justice Scott Baker, sitting in London, rejected the women's claim – on behalf of all the victims – and refused leave to appeal. He said: "The real complaint in the present cases seems to me to be that the Secretary of State paid inadequate regard to the damage to public confidence created by the regrettable behaviour of both these doctors. It is clear from a consideration of the ... evidence that in both of these cases he had this important matter well in mind."

Human rights issues did not apply, the judge said, adding: "There is no legitimate expectation that because the Government has ordered public inquiries into other disasters in the past there would be a public inquiry in the Neale case."

During an earlierhearing, the judge was told that the victims had no confidence in government proposals for "full and independent" inquiries, attended by victims but not the public. The women wanted publicity so lessons could be learnt and public confidence restored in the NHS.

Edward Faulks QC, appearing for Mrs Howard, 23, from Ashford, Kent, and nearly 50 other former patients, said that – despite complaints – the doctor assaulted women from the 1980s until he was jailed for four years in December 2000 over 13 counts of indecent assault, involving 10 women.

Richard Lissack QC, for Mrs Wright-Hogeland, 50, from Kirkbymoorside, North Yorkshire, and the 250 other victims in the Neale case, told the court they had suffered "the cruellest form of clinical abuse". The gynaecologist bungled a series of operations that ruined the lives of many patients.

He was found guilty of serious professional misconduct for botching surgery over nearly 15 years in Britain, having earlier been struck off in Canada. He was barred from practising in July 2000.

The judge said the women would have to ask the Court of Appeal to consider their cases.