In short: No.
The word nation refers to the people within the country (and technically outside too – at least those who share their identity), so the religion of a nation is the sum total of the religions of all the people within that nation.
According to the last census, approximately 60% of Britains put themselves down as “Christian”, which means that on the surface 40% are not Christian (and nearly 25% of the total are “not religious”).
But there is quite a good chance that a significant proportion of that 60% are not fully Christian in the sense that it may be easiest just to say “Christian” when asked without really meaning it. Particularly in smaller communities (and there’s still a fair number left), a lot of community social life is associated with the church.
And a lot of older people will remember a time when choosing “Church of England” was the closest you could get to choosing “No religion”.
But even if 60% of the population is Christian, then we still cannot say that Britain is a Christian nation – too many people belong to other religions or none at all and claiming that we are a Christian nation excludes those others.
But is Britain a Christian state?
Well yes, and no.
The Church of England is an established church; whereas the Church in Wales, and the Church of Scotland are not. Meaning that if you live in England there is an official state religion but in other parts of Britain there is not. To add to the confusion, the Church in Wales is a daughter church of the Church of England.
But whilst the Church of England is an established church, most of the rights and privileges of an established church have been stripped away over the years. The remaining rump of rights is rather negligible with one exception – the head of state is also the head of the Church of England.
But the monarch has rather less power in reality than in practice. The current queen could in theory dissolve parliament at any time she chose; in practice parliament is most likely to ignore her wishes. Similarly if the queen were to start interfering with the Church of England, the Archbishop is likely to politely but firmly ignore her.
Similarly being a member of the Church of England does not in practice give you any special advantages; nor does a non-member suffer any significant disadvantages. The only disadvantage I can think of is that if I were somehow to become a candidate to become the next king, I would be excluded from the succession because I’m not a Christian; but there are other far more significant obstacles.
But is our culture influenced by Christian values? That is an impossible question to answer unless you specify which values and allow me to point out that many so-called Christian values are in fact values shared by anyone without regard to religion.
We do have a Christian past. And a pagan past. And many other influences from the past. All of which influence the values of Britons today.