The European Convention on Human Rights is the main barrier as it's the one the Govt cannot easily avoid.
ARTICLE 8: RIGHT TO RESPECT FOR PRIVATE AND FAMILY LIFE
1. Everyone has the right to respect for his private and family life, his home and his correspondence.
2. There shall be no interference by a public authority with the exercise of this right except such as is in accordance with the law and is necessary in a democratic society in the interests of national security, public safety or the economic well-being of the country, for the prevention of disorder or crime, for the protection of health or morals, or for the protection of the rights and freedoms of others.
Can it be argued that the mass accumulation of data via the NIR or other data-betrayal initiatives are necessary
for the protection of the rights and freedoms of others?
As you see, that's quite vague. It's possible the mass-surveillance is necessary to protect a couple of hypothetical people from being terrorised, robbed or otherwise have their freedom impinged upon, even if that mass-surveillance means a dramatic reduction of freedom for the entire country.
At the end of the day I suspect it's up to the interpretation of the Council of Europe, which is why I've moved this post to Legal Questions. Even though the Govt has twice legislated in ways that officially contravened the Human Rights Act, we would be stupid to assume they haven't got some kind of answer to this barrier up their sleeve.
There is a similar thread on the ECHR/HRA here