Cold water from both taps only in kitchen
If you have a dedicated heater for the kitchen, then the obvious conclusion is that it broke. Thanks to @ratchet freak for pointing this out.

I had a similar problem without a dedicated heater where the hot tap in the kitchen was slightly warmer than the cold one. I turned the boiler to a higher setting and now it works fine. I have no idea why the rest of the hot water in the house worked fine.