Jo Macdonald wrote:
I've always thought in British English.
But don't take my word for it.
I don't always trust the spell-checker, it's certainly not infallible.
From:
https://www.grammarly.com/blog/program-programme/ In American English, program is the correct spelling. In Australian English, program and programme are both acceptable. In British English, programme is the preferred spelling, although program is often used in computing contexts.
Decades ago, program appeared in American and British writing. In the nineteenth century, the Brits started to favor the French way of spelling it—programme.
That's how I see it as well. Nobody at IBM UK, where I was once employed sometime last century, used the spelling 'programme' in an IT context. At least nobody I came across; obviously I cannot certify the absence of rebellious elements, such as a disgruntled employee secretly scribbling 'programme' on scraps of paper in the loo before flushing the evidence.
As it has already been pointed out, 'programme' is a French import. In French, the only purpose of '-me' is to avoid the A being nasalised. As nobody would nasalise 'program' in English, the '-me' is just historical baggage. UK English has simply retained more of the original French spellings than US English has.
As computers were invented, and the majority of software manuals were written in the US, I guess the US spelling became dominant in the field, even in the UK. Computer programmers aren’t linguists and wouldn’t have bothered fretting about the US spelling. In a technical field, it’s also simpler to have just one international spelling.