Family visa

This is confusing.  You need to give more details.

If your family is here already on a dependent visa, the only time you would need to provide those documents is in the case that you didn't take mobility and previous company cancelled your visa (and current company needs to apply for a new visa).  Is that the case?

If so, then there is no way out of it.  LMRA will not entertain application without these documents and you need to get them.  Didn't you provide these documents the first time you brought your family?  if so, your sponsor can try to go to the customer services counter and try to share with them that you are already here with the family since long time and to pick those documents from previous applications.

Yes, I worked 14 years in one company and my family staying here for last 13 years, recently I changed the company, my old employer cancelled my Visa, new employer applied my Visa and its approved. Now to apply my family they are asking for marriage certificate for wife and birth certificate for children, birth certificate I am getting from India, for marriage certificate I told my HR that through embassy me & my wife both together give a affidavit certificate certified by embassy, he said it will help.

Also, i will ask him to go and meet LMRA  customer care as suggested by you.

Thank you for your informations

1st time it was 2006, during that time, I just gave my family passports, wife passport having my name in spouse and children passports bearing my name as father. Apart from, I didn't give anything. Those time there is no LMRA, everything through Nationality, passports &Residence Affairs, MOI.

Yes makes sense.  LMRA is new and  does ask for more documentation.