A feature of the British Museum collection database is that you can build a SPAQRL query to return the collection data in a different and machine readable form.
So if you head to http://collection.britishmuseum.org/sparql and enter…
PREFIX crm: <http://erlangen-crm.org/current/>
PREFIX skos: <http://www.w3.org/2004/02/skos/core#>
PREFIX thes: <http://collection.britishmuseum.org/id/thesauri/>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
SELECT DISTINCT ?object
{?object crm:P70i_is_documented_in <http://collection.britishmuseum.org/id/bibliography/294> ;
crm:P128_carries / crm:P129_is_about ?satire .
?satire skos:inScheme thes:subject;
rdfs:label "satire"}
…you get a list of metadata for everything in the Catalogue of Political and Personal Satires Preserved in the Department of Prints and Drawings in the British Museum. Next step, to figure out how to meaningfully interpret at scale the curatorial descriptions therein.
My thanks to the Barry Norton at the BM for building this query.
cradledincaricature 
This query is slightly more specific than “everything in the Catalogue of Political and Personal Satires Preserved in the Department of Prints and Drawings in the British Museum”. It finds everything in that catalogue, then narrows down to those items that are classified as about or carrying ‘satire’.
This gives 22485 results. If you don’t restrict to items that have the ‘satire’ heading, you get a slightly larger 23290 results.
Ah yes: removed lines 7-9 (keeping the the final curly bracket) and I do indeed get 23290. That is what I want. Thanks Owen!