I did a worktop using this method with a jigsaw and a fine blade.
For the "receptive" half of the join I carefully marked out the main cut and the intersecting 45" cut - made the intersecting short cut first then the main one. (cut from the underside of the worktop unless you have a down cut blade for the jigsaw). Then simply cut the matching corner of the end of the other half. Finally I routed a 1/4" slot into the mating ends of the worktop - added wood glue and hammered in a wooden lath (a long biscuit if you like). Fitted the first half of the worktop in place and then tapped the mating part of worktop into place using a club hammer and a bit of scrap softwood to protect the end of the worktop. The join was not as "perfect" as you will get with the template - but a good deal less unsightly that those nasty joining strips!