In the UK the Building Regulations require that branch pipework for WC's
should be a minimum diameter of 100mm if the WC outlet is greater than 80mm
diameter, or 75.3mm if the WC outlet is less than 80mm diameter.

This all sounds promising.

The internal diameter of my wc pan spigot is 77mm and outside diameter
is 107mm. It's an Ideal Standard design called 'Compact'. So from what
you say I can use an 82mm soil pipe.

In reality, the smallest pipework available in the UK for WC branches is
82mm diameter. 82mm soil pipe and fittings are stocked at some plumbers'
merchants.

I think I can just about squeeze 82mm pipe between the plasterboards
of the stud wall. Now I just need to track down a supplier of the
parts.