Found an article at majorca.info saying that of all destinations Mallorca and Palma is where most britons hire a car for holiday. If this is the case you probably know about most care rental places already, but if not here are a few present online.

Hasso Rent a Car
AutoEurope
Record Rent a Car
Europe Car
Mallorca Car
Gold Car
Autos Roig
Sixt
Argus Car Hire
Gesman Rentacar (added 2011-07-09)