Most likely, because the boat was built before 1990 when Mirrors became an International class. After that point all boats (starting with boat 69070) had to carry an ISAF (or IYRU as it was then) blue and white plaque.
The first GRP Mirrors were produced in March 1986 for Bell by Ferranti. At that time sail numbers were 68076 and above. They are easy to spot, they had "hollow" topsides (i.e. the hull sides above deck level) and very rounded corners inside the hull where the topsides meet the aft and the bow transoms. There is a fuller discription here.
Some of these boats had wooden thwarts, and these have the sail number etched on the thwart.
Bell Ferranti Mirror number 68849 - thanks to Trevor Wilson for the photos.
On the boats with GRP thwarts the sail number was not stamped on the hull, and for whatever reason, Bell's choose not to put a sticker with the sail number anywhere on the boat. That means if the original sails are lost, or if the numbers have come off the sail, there may be no way of telling what the original number is. If you have one of these boats, it might be worth looking very careful to see if there is any tell tale sign of what the number was. If you have some paperwork, that's the best place to start. If not, look on the mainsail, and spinnaker if it has one, for signs of where the numbers where. You might see traces of glue, or the sailcloth might be less faded,.... Look at all the other bits of gear, you might find something there. If it's a Bell/Ferranti the first digit would have been 6 and the second one 8, so the sail number will be 68nnn. That means you only have to work out the last three numbers
If you own one of these boats and you really want a number, you could apply to ISAF for a plaque, but if you don't know the number, you will have to pay the builder's fee again as if it was a new boat, so that's quite an expensive option. The upside is that you would get a new 70,000 series sail number. On the other hand, if you can find sufficient evidence of the number, ISAF will issue a replacement plaque for a few pounds.