If you find Polaris, you have both a vector to north and an angle to calculate latitude. No other info needed for that.
So you only need 1 overhead star plus a clock to figure out approx longitude.
Magnetic north is only useful if you need help finding Polaris.
For celestial objects, The math is rather simple. It is the intersection of 2 circles. The refence between the two objects would resolve which intersection is the correct one.
For magnetic north and 1 celestial object, the math is much more complex. Magnetic declination changes depending on where you are. You have to know roughly where you are before you start using it.
Polaris is important because it doesn't move, relative to the rest of the sky rotating around it.
You measure the angle from Polaris to geodetic "up" and that's the complimentary angle to your latitude. There is no complex math, just 90-x=y
If you have the time in London, and can observe the sun at its peak (solar noon) then you have longitude (after converting hours to degrees, and keeping minutes and seconds).
Or with an almanac, you can measure pretty much any known ID'd star or the sun at any time, and look up longitude from that.
Reinventing the wheel isn't needed, it's been the same process for centuries.
With two points that should narrow down the position to two possible locations (with rather large uncertainty).
Edit: thinking about it further knowing north would reduce it down to 1 point. You also need to know where you are in the world to know which way magnetic north is pointing. It would be 1 very fuzzy spot.