We own two companies registered at our address and are receiving all kinds of junk mail addressed to these companies. Is it possible for us to opt out of receiving such mail?
Unfortunately, it's not possible to opt out or otherwise force the senders to stop sending junk mail addressed to your companies. The opt-out scheme for addressed junk mail, Mailing Preference Service, only allows you to register individuals at residential addresses, and it's not possible to stop 'business-to-business' junk mail using data protection notices (because the Data Protection Act only cover personal data). There's one exception when it comes to data protection notices though; if you're a sole trader you can use the notices (because as a sole trader you are the business).
That leaves you with two options: you can politely ask the senders if they can take the businesses off their mailing list and you can return the junk mail to the senders. Both are purely informal ways of stopping junk mail, and there's nothing you can do if the junk mail keeps coming.
For information, you can register your address with the two opt-out schemes for unaddressed mail: the Door-to-Door Opt-Out and Your Choice. The latter scheme only allow you to register personal address, but because your personal address is the same as your business address you should be fine.