Alan, I think that you have that the wrong way around. See Fig 3A4 and 3A5. (In the Big Brown Book they are on the same leaf, but in the Big Blue Book they sit nicely one above the other when opened.)

Type B will trip "instantaneously" at 5 x nominal, whereas type C will trip at 10 x. The rest of the curves are similar.

Typically a motor's start up current is 6 x nominal (at the least the ones which I have), which would cause "nuisance tripping" with a type B MCB assuming of course that the rating of the MCB matches exactly that of the motor.

I feel sure that the manufacturer's instructions (which you do not have at the moment) will clarify matters.

(I am surprised that you cannot easily find a type C MCB.)

Further to that - the slow thermal part of all breakers B,C D W Z of a given rating is pretty much the same - a 10A breaker will carry 10 A all day, and the thermal part trips off at twice that current after a what seems like an eternity but is in fact some minutes. This emulates an old fashioned hot wire fuse pretty much - the higher the overload ratio the faster it operates.
What varies by letter group is the near instant operating magnetic part - that of course the fuse does not have.

So looking again at that 10A slow bow part, a B10 adds a magnetic part set up for about 30A and may go anywhere between 20A and 50. The C10 type has a coil with fewer turns, and is set to instant trip at between 50 and 100A, the D type higher still (100A to 200A )etc. Then there are the trick sizes W K and Z that no-one uses if they can avoid it that have the wholesaler sucking through his teeth and  wondering how much he can mark up the price- these are just slightly tighter specs  and in most cases a B will do for a Z and a D for a K, but not always.
So for a motor with inrush, or indeed lamps with inrush issues, a C type is less likely to pop out when unexpected, and a K or D type less so still.

note that another way to look at this is to realize that the magnetic bit of a 32A B type is more or less the same as that inside a 16A C type and the same coil could also be fitted to an 8A D type if such a thing existed...

regards Mike.
This graph with time up the side and overload multiple along the bottom may help.

PS having said that an 8 amp D type does not exist, blow me the Eaton catalog has it ,and also  breaker type 's' I have never heard of before.. Live/learn and all that. A designation just asking to be confused with an S-type RCD is you ask me but there you go!

Thanks, long day, eing lazy and not looking in books :-(. Sorry for wasting your time.

The board is from a company called Live. There are a few stockists. I am sure i will find the parts, just wanted to avoid another 10.00pm session placing orders.

Had two orders I placed on Sunday go wrong because supplier wasn't showing accurate stock levels, need to fix both of them now.

After a bit more research I am less confident I am going to get the part quickly. May have to persuade the customer that he is going to have to replace the bargain basement board he bought. Hopefully I am being over pessimistic.