Women who are concerned about their breast implants made by the French scandal-hit company PIP should be able to have them removed for free, either by the NHS, if it is reconstruction after breast cancer, or by their cosmetic surgery clinic, the government has said.

There is no evidence that routine removal is necessary, said the government at the end of an expert inquiry into the safety of the implants - which were filled with industrial-grade silicone intended for mattresses - but it accepted the argument that many women were distressed and anxious and did not want to wait for a rupture to occur.

The government gave a pledge to the 5% of the 40,000 women who were given implants made by the French company Poly Implant Prosthese (PIP) that they could have them removed with no charge. It cannot require the same of the private clinics, but said it expects them to make the same offer. It is unlikely, however, that they will offer to replace the implant for free.

A Department of Health statement said "the NHS will support removal of PIP implants if, informed by an assessment of clinical need, risk or the impact of unresolved concerns, a woman with her doctor decides that it is right to do so".

"The NHS will replace the implants if the original operation was done by the NHS."

The statement went on: "The wellbeing of women who have had PIP breast implants is our main priority. That is why the health secretary asked an expert group – led by the NHS Medical Director, Professor Sir Bruce Keogh – to review all available evidence and data on PIP breast implants.

"The group has concluded that the advice given by the MHRA still stands and that there is not enough evidence to recommend routine explantation of these breast implants. The group also agrees there is no link with cancer."

"However, it is undeniably the case that these implants are made up of non-medical grade silicone and therefore should not have been implanted in women in the first place. We recognise that this will be worrying for women with PIP implants and that they need to be properly supported by those that performed the implantations."