Could well be the ignition switch or anything else in the circuit, will it start after several turns of the key or do you have to do something else? If operating the switch a number of times makes it work I would go for the switch, if not could be the auto inhibiter switch, in which case moving the gear lever may bring it to life.

Why not try connecting a bulb to the starter motor supply at the solonoid. Next time it fails to turn over, see if the bulb lights. If not, progressively move th light connection back up the circuit untill you determine which component is causing the issue. Cheaper than substitution by guesswork.

If you want a faster diagnosis, why not connect several bulbs to the different parts of the circuit and label them. Then next time the problem occurs see which doesn't light to determine where the fault lies.

Of course, if they all light and it won't turn over it's the motor unit (only test the solonoid and motor seperately if you can replace them seperately - usually they come together as one item).

If you need a new starter I can thoroughly recommend SAC in Coventry. They recently built me a recon alternator on a Saturday morning whilst I drove over there.