The short answer is probably no. Having watched a programme on Sunday night asking that question, it seemed pretty clear that it's not the case. As the Archbishop of Canterbury has wisely suggested, we need to keep a sense of proportion. Much worse things happen to Christians elsewhere around the world. But much more than this, you can only really consider something persecution if you are prevented from doing something because of something you are or choose to do without good reason. Not being allowed to wear a cross at work doesn't constitute persecution because you don't have to take the job, nor is essential to wear a cross. If they were saying you could never wear a cross, even in your own home, or if they were saying you couldn't have ginger hair at work, then that would be more like persecution.
More realistically, you could say that Christianity is being marginalised. Things that were once the norm no longer are. Beliefs, values and practices are changing, and no longer are things that are, to some, deemed 'Christian' held to by the majority of the land. However, a lot of the people bemoaning this fact don't even follow Christ as their king, and so are more concerned with preserving their own culture than about anything else.
The important question is how do Christians respond as things start to change and these values and practices are no longer considered the norm? On the one hand you can become defensive, inward-looking, and ultimately very selfish, seeing the Christian's role as 'defending the faith', hoping that we don't become infected by the rest of society. On the other hand you can seek to be like Jesus, grounded in your identity in Christ, outward-focused, caring for others, focused not on outward practices but on the underlying worldview of people and their need to know and follow God.
OK, so 'Christianity', or at least its cultural façade, is retreating from mainstream society, but do we feel sorry for ourselves and look inwards, or do we look upwards and outwards, trusting in God, and seeking to know Him more and to make Him known to those around us?
