.toFloat() giving incorrect anwsers
It seems the toFloat() method is being a bit sloppy in its conversion.
The float closest to 51.507401 is 51.5074005126953125, which is only
0.13 ulps off. The number you got is the float right before it,
namely 51.507396697998046875, which is 1.13 ulps off. Alas, the
avr-libc functions atof() and strtod() make the same error.
I would suggest first considering whether the error is really
significant for your application: it is only about 48 cm on the
surface of the Earth. If this level of accuracy is relevant for you,
then follow Majenko's suggestion and use an integer count of
microdegrees.