Lynton Crosby. Photograph: Andy Hall

The London Mayor came to power promising greater transparency and accountability in the conduct of City Hall affairs, yet he seems to regard the endeavours on the premises of his controversial Australian election campaign strategist Lynton Crosby as exempt from this fine principle.

It recently emerged that between February and July of this year Crosby, an aggressive right-winger best known for sending "dog whistle" messages to voters on emotive issues such as crime and immigration, had at Boris's personal request wrongly been issued with a City Hall security pass that gave him access to all areas of the building. This raised a number of questions, not least about how Crosby had spent his time while given the freedom of Norman Foster's glass orb.

Last month, Labour London Assembly member John Biggs asked Boris "how many times and on what dates" Crosby had met him at City Hall. The written reply was as follows:

I meet all sorts of people in City Hall and across London.

Not very transparent. This month, Biggs invited Boris to actually answer his question. Boris's response is he has "nothing further to add" to his previous non-answer.

It's easy to see why Boris might find all this embarrassing. The entire affair has been characterised by misjudgment, disinformation and, critics would say, a cavalier disregard for rules.

In July it emerged that Crosby's pass had been withdrawn, and by none other than the Mayor's own chief of staff Sir Edward Lister. The reason was that only persons involved in "GLA or GLA Group business" should possess them. Campaigners for Boris's re-election do not qualify.

My initial inquiry about how the pass came to be issued produced an answer so completely implausible that mayoral contacts later felt obliged to acknowledge this, intimating that the error was actually down to Lister's predecessor, the late Sir Simon Milton. I was also assured that the pass was not the type that gave Crosby access to the offices of the mayoral team and the GLA bureaucracy.

This too turned out to be wrong. It was Adam Bienkov, pursuing the matter through Freeedom of Information, who learned that although Sir Simon had signed off the pass he had done so because Boris asked him to. Bienkov also reported that the pass gave Crosby access to all areas of City Hall, rather than simply making him exempt from security procedures at the entrance to the building as I had been led to believe.

John Biggs considers Boris's attitude to his questions "outrageous". Certainly, there is a nose-thumbing quality to his replies that sits uncomfortably with those election pledges to be the very model of probity and accountability. And, of course, the more Boris refuses to discuss any meetings he may have had with his re-election campaign chief on City Hall time, the more people will ask if he has something to hide.