Sort of, it’s quite roundabout.
We sold the technology to the Italians who developed it further in parallel with their own design. It’s very similar to that in the 221 Super Voyagers, and the system in the 390 Pendolinos certainly has its origins in the APT, but far more distantly.
The 225 (comprising a Class 91, mk4 coaches and a DVT) likewise isn’t really derived from the APT – not least the APT was designed for the curving WCML (hence the tilt) whilst the class 91s were never designed to tilt as it’s less beneficial on the far-straighter East Coast Main Line. 91s were designed before the APT had been withdrawn; the Intercity 250 was the more obvious spiritual successor to the APT, but that too was canned before production ever began. Confusingly the mk4 coaches were designed with tilting in mind (there’s a taper on the body ends to avoid them hitting lineside structures) but it never came close to fruition.
Once the APT faltered we continued with the class 86 and 87 electrics with mk2 and mk3 coaches which preceded the APT. Class 90s came along in the late 80s, still hauling the older stock, and ultimately nothing changed until the Pendolinos appeared in the early 2000s.