One possibility is that you have a 1071 crank, the other is that your pistons are short, the third is that your rods are too short.
The 1071 was introduced first. When the 1275 was introduced the block height was increased to compensate for the longer stroke. For the 970 the rod length was increased. So if a 1071 crank is put into a 1275 block the pistons will be below the top of the bore. (I've no idea what happens if you use a 1071 crank with 970 rods in a 1275 block).
A 1071 crank should have the number AEG 171 (see
http://www.hotbricks.org.au/techtips/ar ... cranks.txt for a list of the 1275 possibilities)
Short pistons seems a remote possibility if they were sold as Mini pistons. Putting Hillman Imp pistons into an 1100 Mini had this problem as the Imp pistons are shorter (i.e. between the top of the piston and the pin, not the overall height) than Mini pistons. Imp pistons won't fit a standard 1275 block however (either 68mm or 72.5mm diameter depending on type). If the pistons didn't come in a box marked "Mini" then maybe they're from some small Korean or Japanese car.
Short rods seems even more unlikely, since the only conceivable use for them would be to put a 1275 crank into a 1071 block or, as noted in an earlier post, to create an engine with stuff-all compression.