Hi, thanks very much for your question. My name's XXXXX XXXXX I'm going to assist you with it.
Whilst Equita is an official bailiff company used by TFL (see a list of their bailiffs here: http://www.tfl.gov.uk/roadusers/congestioncharging/12077.aspx), they can get information wrong, which appears to have happened on this occasion.
You have acted appropriately in asking the police for advice and the police have given you the correct information. This should be fairly straightforward to resolve once you are armed with evidence to show that you are the owner/tenant of the property at the address.
You need to contact the company without delay using one of the contact numbers on their letter. Provide them with the relevant reference number and inform them that the person referred to on their letter/s does not live at the address and that they need to update their records. Follow this up in writing along with evidence that you live at this address.
If you have any difficulty you can write to the Court and enclose their letter and your letter in respose. However, I would very much hope that this would not be necessary once you have approached the bailiff directly.
I appreciate that this can be very worrying, however bailiffs cannot generally enter by force and are strictly regulated with respect to the actions that they can take. To give you some peace of mind whilst you are resolving this, please find some information on what they can and cannot do here: https://www.gov.uk/your-rights-bailiffs/what-you-can-do-when-a-bailiff-visits
I hope that's helpful and, if you require any clarification please don't hesitate to let me know.