Starter motor not turning - possible fuse/relay?

Hi there, just seeing if this rings a bell with anyone. MG-TF160 model year2004, VIN number ....623687. Starter motor suddenly stopped turning with no warning, and I cannot hear any click from the solenoid. Never had an issue with it before (car owned ~3years) and it had started fine that morning, we went for a run (~30miles), stopped for 5min to consult Google maps, then 'nothing' when I turned the key. Dash lamps all normal (except the EPAS warning light which stays on when I turn the key to the ignition position - never done that before I believe). Gave the starter a bang with an extension bar, still nothing. Gave the car a shove and it started fine with a push start, drove home and parked up.
Yes, the battery voltage is good (new unit ~1year ago), I have a 12V plug-in USB widget that displays the voltage so I always have an eye on it. Have checked the relay in the boot (by swopping it for another, then for a new one I had). I have seen some references to a 10A fuse that protects the circuit but I can't see it on my map of the fuse boxes under the steering wheel or the under-bonnet box. No obvious blown fuses or fusable links in the under-bonnet box.
I have bought a new starter motor as I was wanting an excuse to change it anyway (no idea how old it is, possibly the original!), but something is telling me something else is at fault given the lack of warning and not even a glimmer of life from the motor or solenoid.
I really appreciate your taking the time to read this, and hopeful for some helpful responses!

Hi, I have just had a quick mooch around for solutions to this problem and as a starting point I would put a multi meter on your battery to check the voltage and then clean the contacts on the starter motor.

First things first……. Check the terminal on the starter motor

Stick your hand down by the charcoal canister & you'll find the contacts for the starter motor, give those a good waggle & see if that helps. If that works, obviously change the terminal, it's a large lucar/faston, in actual fact next time you're under there Change it any way, it'll cause you problems one day.
M