I have managed to achieve a reasonably good repair of a similar small dent by filling it with layer upon layer of enamel paint of the same colour as the worktop. The enamel is about as hard-wearing as the original surface so I expect the end result to be a permanent repair, However, a roughly 2-3mm deep dent did need about 10 coats of paint. Each drop of paint had to be wiped flat and then allowed to dry thoroughly before applying the next, before all signs of the dent disappeared. Any excess paint which gets on to the undamaged surface of course has to be wiped clean immediately before it has a chance to dry.
It' may be worth trying. It'll certainly be the cheapest alternative even though it's a bit fiddly and takes a bit of time to get the desired result.