Yeah why not rely on an unregulated company like Paypal which is not considered a financial institution in the UK, not a bank, not a credit card company and not regulated under the FSA? ;). At the very least if you use Paypal, use a credit card with them for some protection.
If you pay via credit card direct with CRC it goes via the card company payment processing system, just like most web sites these days. No details stored with CRC and they don’t have access to them. http://www.chainreactioncycles.com/Information.aspx?TranslationLargeID=6#wheels
PayPal credit card payment without logging in is much the same but potentially with less protection (or at least if you needed to claim it would involve the card company attempting to claim against PayPal). If you log in and use PayPal funds or the default funding via bank debit, then you have very little protection at all.