My desktop is a factory standard HP m9451uk (link to specs below).
I have just bought a Geforce GTX550ti graphics card to upgrade it a bit. The current power supply is 300W but the card says to use a minimum 400W supply.
I'm not planning on running multiple monitors and my max resolution is 1600x1200, I do intend to play games like Crysis 1,2&3, Skyrim and Napoleon Total War on high graphic settings (if not highest where possible). Do you think my 300W PSU cope? If I try and it can't cope, could it damage other components?
With OEM PCs like that one you're generally given what you need to run whats in the PC. I wouldn't trust that PSU with the addition of a 550ti. You might want to look at getting a decent 400w or better PSU.
Corsair, Seasonic, PC Power and Cooling - all great brands. For the GTX 550ti 400 watts would be, however, if you buy a quality PSU you may choose a better more powerful PSU (600 Watt) for future use in this or your next rig.