I've also got a Konica-Minolta scanner (a DiMAGE Scan Elite 5400, FWIW) that can scan Kodachromes with no problem. I use it with
VueScan under Linux. With that combination, the IR filtering (VueScan's equivalent to ICE) usually works well on low filtering values, but sometimes produces flaky watercolor-ish results when set to high levels of filtering.
Note that my scanner is a pretty high-end model (among consumer-grade scanners, anyhow; I'm sure it can't hold a candle to a professional drum scanner), and it's last year's model, too; it's been replaced by the next model in the line.
If you're not up for buying an expensive new scanner, lots of services will scan slides, including Kodachromes. I can't suggest a specific lab in the UK, though. If you don't get any specific suggestions, try either a Web search (try searching on "slide scanning service" or something similar) or ask at local pro labs. I'm sure that the better pro labs will be able to produce analog or digital prints and/or good-quality scans, or at least point you to an outfit that will do so.