Thanks guys. Great info.
The pump seemed to blow the fuse during "spirited" driving (read that pedal to the floor) when the pump would be trying to keep a HIF44 full, but lesser driving would be fine. I suspect the 3A fuse was threshold but wouldn't sustain the pump working harder. The pump isn't that old but may be getting stiffer with age or insufficient use.

The early Mini electric SU pump had no fuse.  I suspect that when you added the circuit and the fuse you probably used 16 AWG which is rated for about 13 Amps.  Your fuse is there to protect the wiring, not the pump.  Therefore, I like Bill's suggestion of something like 7.5 Amps.

Keep in mind that the ratings of U.S. fuses (glass and blade) are not the same as Lucas fuses.  Generally you multiply the Lucas fuse rating by 0.6 and then select the next lower, closest modern fuse value.   For example, a Lucas 35 Amp fuse would be replaced by a 20 Amp modern fuse (35 x 0.6 = 21)

 might try 7.5 amp.. but sounds like you have short in it..laterbc

Finally had time/weather/excuse to align and let me out for a romp in the Mini.
Lots of power and pep until.... it stumbled and died as if out of fuel. Avid readers will recall this happened to me earlier this season on another Sunday. That time it was finally traced to a blown fuse for the electric SU fuel pump. So, this time, I knew where to look FIRST. Sure enough the fuse had blown. Strange that it takes a few miles before it goes.
The existing fuse was 3 Amp.  I "upgraded" to a 5 Amp fuse and continued on my errand. No problems for the rest of the trip.

The question: does anyone know the current rating for the SU electric pump and what size fuse is appropriate. Note this is an added, separate circuit with its own in-line fuse holder.

Side-note: Today I picked up a package of fuses that "glow when they blow" - appear to have a tiny LED in parallel with the fusible link. Would be handy in the standard Mini fuse box. Not much good in an opaque fuse-holder though.