Is there any way of testing whether it is the solenoid?
Yes, with the car out of gear (obviously) short over the two big main terminals on the solenoid (anything metal and insulated at one end like a screwdriver) mounted on the inner wing under the washer bottle (it just lifts out) and at the same time have a helper sat in the car starting it as you would normally.
I also had to do this for about a week years ago, when the solenoid started paying up (ah, I'll be fine) and then died complexly leaving it the only option to start the car to get to and from work (did get some right dirty looks, especially pushing the mini off a petrol station forecourt to then jump start it and drive off) , until I finally managed to blag a free working replacement from down the scrap yard.
Edited by 1984mini25, 08 September 2014 - 10:16 AM.