Firstly you should check that your builder was/is NHBC registered.
It is unlikely your home does not have NHBC warranty in force otherwise you would not have got a mortgage on it.
If the home does not have NHBC cover yet was marketed as such contact the NHBC immediately.
You should also write to your local trading standards department, as this would be a clear case covered by the Property Misdescriptions Act 1992
If the builder has not completed all the items noted by the NHBC Inspector during the Final Inspection, this may be why the policy is being withheld or it could be something more serious or even just some paperwork that has not been completed.
Your solicitor should be dealing with this. He should not have completed on the sale without the NHBC Buildmark warranty documentation.
He is also at fault and you may like to suggest to him that if he cannot get this resolved you will complain to the Law Society and/or sue him for professional malpractice, especially if you now have an unwarranted new home that has a serious defect.