I moved office so only have a 2,5 miles commute, had an old set of wheels so a cheap cassette, second hand rotor and 1.3 conty sport contacts and I have a commuter. You should be able to get a cheap spare set for sub £100 I would have said. I’m around 30seconds quicker on slicks (about an 11-12 minute journey) but arrive a lot less hot than if I use normal tyres
One thing to watch for is ice on the roads in winter, sounds obvious, but I was happily riding to work when it was a bit ‘brisk’/. Didn’t even cross my mind there might be ice about till I hit the ground really hard right on the point of my elbow…still hurts 2 months later. Oh and buses/drivers seem to regularly try to kill you during winter.
Will be walking next winter, not sure it’s worth the risk tbh.#