"I have put one 256MB module in an old Evesham Micros P11 and it seems to have increased the 'identified' RAM from 128MB to 224MB (?) "
That seems to indicate it has 32Mb on board graphics ( no graphics card ) 224Mb + 32Mb = 256MB. Or you have another memory module in and the onboard graphics has increased with the extra ram.
"The other 256MB module was put into a Mesh PC which had 2 x 64MB modules in, with a third free slot. That PC is now showing 384MB of RAM in Control Panel/System. "
That one is showing correctly.
"Does this mean that both modules are OK or can a PC see RAM even if it's faulty? "
It showing that the ram is seen, but it could be faulty. Because you have got the memory working in both machines, it may be worth running a memory test on both machines to see if there is any faults.