For the last 4 days my phone has (almost without fail) lost its signal everytime someone phones me or I phone them.. Almost as soon as I recieve a call, it's not just in a certain place but everywhere I go.

Is this more likely to be my iPhone or the network?

Unlikely to be the network, but I would ask for a new sim card and if you explain the situation it should be free.

If that doesn't work I would try a factory reset, and if it keeps happening then you'll have to contact the phone manufacturer about a warranty claim and get them to look at your phone.