Check the SPD manufacturer's data sheet.
There is always some sort of over-current protection specified but it can be as high as 315A fuses in some cases, or as low as 32A MCB in others. It can also depend on just how the connections to the SPD are made, say if "V-wired" with the load current flowing through the SPD's terminals, or if the SPD is spurred of a terminal block.
It might be met by the supply fuses so nothing else is needed, otherwise some fuses or MCB would be needed.
Remember that SPD need short low inductance connections to be effective, as well as a minimum cable size for the surge I2t heating effects. So a fuse is probably better than a MCB on that front, and if selecting a MCB go for the C or D curve ones to reduce the inductive aspect of the "instant" magnetic trip. UK regs have max 1m total cable length, ideally less than 0.5m, so SPD within 0.25m of the supply and main earth terminals including any OCPD route.
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