How to tell if your walls already have cavity insulation
Look for a regular grid of small patched holes in the mortar joints, check what the EPC says, ask for a guarantee, and for certainty have a borescope inspection, which looks inside the cavity through a small hole.

Patched drill holes
Retro-fitted cavity insulation leaves a pattern of filled holes, usually about a metre apart. They can be hard to see on weathered brick, and they do not prove the fill is still there or complete.
The EPC
An EPC may say 'filled cavity' or 'as built, no insulation (assumed)'. Assessors do not always open up walls, so an EPC can be wrong in either direction.
Is it a cavity wall at all?
Victorian and Edwardian terraces like the street pictured here are usually solid brick, which cannot take cavity fill. Solid walls need internal or external wall insulation instead.
Guarantee and records
CIGA can confirm whether a property has one of its guarantees and issue a duplicate for a fee. Building control records may also show a notification for the work.
Related services
Sources: CIGA: the CIGA guarantee; Energy Saving Trust: cavity wall insulation.