FYI - You are unlikely to get a helpful response here. Most posters are from North America and the codes are totally different here. I'd suggest trying to find a forum that is more "United Kingdom" centric.

We have a 240V supply here in NZ, and a 2.5mm2 circuit would be breakered at 20A. So what you are proposing is technically sound and would be legal in NZ or Australia.
The 4.5kW rating will only be what it draws at peak, not the steady-state load.

In the USA, cables must be suitable for the amperage, voltage and the environment in which it is installed. The terms used to describe your cable are not used here and so I do not know about that. The 27 A meets the requirement for amperage.

FWIW, 2.5mm2 is very close to 12AWG.

Shouldn't someone installing a 4500 watt coffee machine, in what is obviously not a residential setting, already know this??
Anyone qualified to do this would would not have to come to a homeowner DIY message board to find out how to do their job.