Eh? How does that work? Either the data is publishable or it's not. If it's not something that the world should be able to see then it shouldn't be published in the first place.
For the insurance (MIB) database check:
Data Protection Declaration and Vehicle Ownership Statement
I am entitled to the insurance information about the vehicle detailed above for one or more of the following reasons: It is either registered/ owned/ insured by me or my employer; I am permitted to drive it; I am an Insurance Broker or agent and acting on behalf of my client.
I understand it is an offence to wrongfully obtain information of this nature without any of the above reasonable causes. If I fail to provide true reasons for acquiring this information I may be committing an offence of unlawfully obtaining data contrary to section 55 of the Data protection Act 1998. I declare that the information provided will not be used for any purposes unrelated to this enquiry.
I confirm that: I have read and understood the data protection declaration, one of the options stated above applies to me and I agree to the terms of use as stated on this website.
No such restriction is given for a tax or MOT enquiry, however.