Hi Soph,
I can't remember exactly how I went about applying for the police certificate but I know it was just a form that I had to fill in online then print out a hard copy and send it to the police with a cheque for the amount they require. As for the letter of good standing I just emailed the HPC and they sent one to me, I'm sure if you ring up they will do the same. You don't need anything from the CSP.
Good luck with it