modern science and technology owes nothing to the ancient greeks. modern science and technology is based on accepting experiments as sources of truths/facts of the universe. ancient greek philosophy which prioritized the ideal explicitly shun any knowledge that could be arrived at by observation (i.e. through our senses). the battle to admit experiments into the criteria of truth was mainly waged in britain, from locke onwards. so, while the ancient greeks bequeathed us the immense inheritance of philosophy and the search after truth, we wouldn't be here if we didn't disrespect their strongest argument that truth arrives by cerebration alone.
If it was, then that culture wasn't British culture but some kind of central-European culture that flourished around the time of the Industrial Revolution. I was in Paris, recently, in the Museè des Arts et Mètiers, and I stood half a meter from a collection of Pascalines, the first machines capable of performing arithmetic operations, created by a Franch mathematician, Blaize Pascal.
Modern science and technology did not grow in one place, or in one go, and in any case, as we all know, it all started with the Greeks, ευχαριστώ πολύ. And then there was the Middle Ages.
[Incidentally, do visit the Museè des Arts et Mètiers and do visit the Science Museum in London, if you can. They are not nearly as well-known as the natural history museums but that just means they're not nearly as crowded. You can find ancient computers in both, it's like they evenly split the spoils of an era of experimentation with automating computation. Paris has the Pacalines and Vaucanson's loom, London has (a model of) the Difference Engine. They have more modern machines also; in London I saw a PDP-10, I believe, in France a Fridden Flexowriter right next to a drum memory. They are places to be lost in, if you like that sort of thing. Also: entire rooms filled with models of steam and hydraulic machines.]