Currently, police chiefs must write to the Commons Speaker telling them if a Member has been held. The Speaker must then alert the House of Commons in official documents – meaning the name will become public.

But the little-known Procedure Committee – a body of MPs which regulates how Westminster works – wants to scrap the practice.

It comes after two Tory MPs in the last Parliament were arrested on suspicion of sex offences. One was charged and later cleared by a jury, while another was not charged. Both were named following their arrests.

An inquiry which started in January today recommended shielding the information from the public. Its report says: “We conclude that the House should continue to instruct police forces to provide notification of the arrest of any Member.

“We also conclude that the present practice of the House in requiring the Speaker to publish the fact of a Member’s arrest regardless of circumstance is, in its generalised and non-discretionary application, incompatible with the right to privacy.”