Alex
That sounds very similar to my symptoms. I initially thought that it was a duff battery, so replaced it - it was better, but no joy. Not knowing whether the car was going to start (hot or cold) was starting to get to me... I then tried to check the contacts to the solenoid and managed to crack the case when loosening the main contact nut (be careful!).
As a result of this, I ended up replacing the solenoid and fitting the 'hot start relay' mod at the same time.
Since then I have had no starting problems whatsoever. The only problem is that I don't know what one thing I did fixed the problem. I suggest doing the relay fix first if the battery volts are OK and if that doesn't work, try taking the starter off, then the solenoid, and cleaning it up. (Oh, and disconnect the battery before you start - something I will only forget once!)
Steve