6mm² is OK (just) at 50m, using a 5% volt drop.

Interestingly, if you went to the 16th edition of the regs (the last one just gone), you had a 4% max volt drop, and this would of meant upping the cable to 10mm² for 50m.

You can drop a maximum of 3% for lighting and 5% for everything else.  IF you have no lighting on that cable run (I don't see underwater lighting as counting), then 5% is the max.

You could only run around 30m at 32amp with a 3% volt drop.

Prices vary across the country.  You would need to allow approx £250-£300 including materials I guess.

Your electrician will likely want to be upgrading your main protective bonding too if this is not up to the required size.