Dan's comments make sense.  I have a 1993.  You may fix your problem with a little adjustment at the slave cylinder on the bell housing.  I've been driving cars with a clutch for 60 years.  I have 4 now, 65 Vette, 72 Porsche 911, 93 Mini and my 2004 Dodge dakota.  I have never replaced/wore out a clutch.  I do change it if the engine is out.  I've learnt to heel/toe down shifts and double clutch in some cases. The old technique of going into 2nd first, you do that at idle rpm, isn't going wear out the 2nd gear synchros.

Dan, you got me again. I've driving a RHD mini for so long I forget there is LHD minis.

6464s suggests a good start, though his procedure is a little confusing and very awkward - IF you have a left-hand drive car. Mine is a leftie, so I could not imagine seeing the clutch linkage actuate from there. Then I noticed he said to use one's left leg. Yes, the clutch is normally actuated by the left foot, but while standing outside the car, that would be a contortion. Isn't it enough of a contortion just to get into a Mini?

Thanks for the chuckle!

Before swapping master cylinders, you need to check all the clutch linkage for wear. Being a 1994 model, your car should have a Verto type clutch, which has a much shorter release lever. Wear in its pivot or at the ball end would have greater negative effect - too much slack.

Search the Forum for "clutch". There's lots of info there.

That is the usual solution for a 3-synchromesh transmission. It does work with a 4-synhcromensh transmission but tends to ignore the existence of a problem. (Yes, technically a Mini transmission may have baulk rings - it is the process of synchronization we are after.)

In a 3-synchro box, with the clutch disengaged, the input shaft the transmission input shaft should not be turning. If it stops so that the teeth of first gear balk (do not mesh), putting the shifter into 2nd gear (which does have synchromesh) usually rotates the input shaft so that the alignment of 1st gear allows the shift.

In a 4-synchro box, with everything working properly, you don't have to use 2nd gear to align 1st gear
 because the synchro on 1st gear does it for you.

In a 4-synchro box where everything is not working properly (e.g. the clutch is not fully disengaging, as in this case), the input shaft continues to turn while the other gears are not, making it difficult to engage 1st gear. By using 2nd gear to stop the input shaft from turning, you would be adding wear and tear to the 2nd gear synchromesh.

We should treat the problem, not the symptom.

Go into second then first . 

You will have to take a look at the mechanical action of the clutch. with the bonnet up, door open, you on the outside of the mini, reach in with your left leg and foot depress the clutch, peek inside the engine and see what is happening. Of course it will be easier if someone sati in the drivers seat and depressed the clutch pedal. You may need to rebuild you clutch master or get a new one.

Clutch fluid is called hydraulic fluid.

I have a 1994 Rover Mini 1275cc with manual 4 speed. I have noticed with engine running it is somewhat hard to get into first gear. If the engine is off, easy to shift into first and all gears. So I suspected the clutch fluid might be low, but it is where it should be at the bottom of the filler. Based on shifting with the engine off being ok, and now clutch fluid ok, is it an adjustment of some sort that I am missing somewhere? Any other ideas of what I should check?