How much does CD player affect overall sound?

While the previous posts are correct, IMO, you can only appreciate quality source components if your downstream gear and speakers are resolving enough to let the better source gear shine. My own experience, in which I upgraded from an entry-level CDP that retailed for $500 to a well-regarded tube CDP that retailed for twice as much, underlined this point. I could not hear a lick of difference between the two CDPs. The more expensive unit went back. Since then, I've upgraded my amp, preamp, and tweaked the system a bit. I am in the process of upgrading speakers now. Once that is done, I will revisit the digital source upgrade.

IMO, your gear is very capable of resolving the differences between CDPs. I would focus on home auditions that allow you to compare your current CDP with others, using familiar discs. If you feel any improvement is worth the added expense, go for it. You can also keep the Cambridge as a transport, and try out stand-alone DACs. Many new models are on the market from well-known manufacturers who have never before offered a separate DAC (Sim Audio, Cary, et. al.) This will give your system some added flexibility for the future. Just remember to use a respectable digital interconnect.

Have fun!

A wise person once told me that preamp, cables, amp or speakers will not PUT BACK what is not there from the start when asked about the importance of a great source.

A lot, but so does everything else. There really is something to system matching. That said, I would have to ask what you feel you are missing that a new CDP would bring to the table.

You’ve got some nice gear, however both the CJ and the B&W’s have a very unique house sound. I have found CJ preamps to be overly dark, and slow (IMHO based upon personal experience with the Premier 3 and the Premier 14). I’ve also found the B&W to be a tab dark for my liking, unless properly matched (based upon poorly executed dealer demo’s).

FWIW, I’d rather have a mediocre CDP with a great pre/amp/speaker combo, than the other way around (a great CDP with a mediocre pre/amp/speaker combo) any day.

Transnova said all and said it well.
Garbage in garbage out!

I usually try to select a component upon the needs of my system's needs first, and my preffs second.

As personal preffs go, I'll vote otherwise for the CJ & BW items the other poster said were 'dark' sounding to hem. I found nothing muddy or unclear with either items... CJPV14 or BW 804s. Not at all.

Perhaps if some other digital sources are in or about to be in the mix, a DAC might be in order to seek out. A great DAC will escalate the perfomance of of and improve upon, the current levels of the now CDP. Albeit a very good DAC IMO begins around $1K new, and goes up from there. So there's that to think about.

What does your rig need? What do you want yourself, sound wise? Well, then, there's your direction.