Yesterday was a long and crazy day! The attempt to discover what was tripping the circuit breaker revealed that it wasn't an appliance - it still tripped with nothing plugged in on the affected loop.
I spent most of the day checking all the sockets on that loop, replacing two and rewiring another, in case they were shorting out but couldn't find the problem. It has to be a wiring issue somewhere so half the house is still without power.
We're going to have to get an electrician in to have a further look and hope they can find it quickly. We're just dreading they'll say it all needs redoing in which case we just hope it's something we can claim for on the house insurance.