Can anyone point me in the right direction with a starting issue?

2001 TD5 Hardtop. I turn the ignition key, and the usual lights come on, all correct, the glow plug light and engine lights go off after a few seconds. I turn to start, I get a 'click' and nothing. This might happen 1-3 times then next try it starts just fine.

I looked at the battery terminals and they were filthy, I good scrub with a wire brush on everything and it then started first time. I thought job done, but no, the problem is the same. I traced the wiring and didn’t find anything loose, but I can only crawl under, don’t have a ramp or anything. It has a new alternator. Could it be starter motor? Just seems odd it, when it starts it starts and runs fine. Any tips?

Did you remove the battery connectors and clean then tighten up , similar issue on daughters Corsa other week with the click , and batt terminal need nipped up

Do you know what the 'click' is ?

It's likely that it is the starter solenoid.
The contacts wear and don't make proper contact so there is not enough current (power) to turn the starter motor/engine over.

Your battery may also be a little flat or you have bad contact with the battery terminals or a bad earth.
If you say what car you have we would be able to advise you where to look for the main earth connections.

All of the above are relatively easy to fix.