CDW needed for car rental in UK?

Is there any reason to buy any additional insurance from the car hire company?

No.

It does look like CDW is already covered by my Chase Sapphire Preferred card.

Be sure to confirm that. Not saying you are wrong, but eliminate the possibility of a nasty surprise.

As was noted, read the fine print on what your credit card is providing (Collision?, liability?, Tires,Glass?) what steps you need to take to make the insurance valid (declining certain types of coverage for example) and if you have a claim, what you need and what the process is (Police report?, Certain Form?, Do you Pay up front then seek reimbursement?)

You may need to call your credit card to get some answers, rather than ask the first customer service person that answers, ask if there is someone that specifically handles claims, or the number of the company that does handle the claim.(Chase likely contracts with an insurance company.)

I have not had a claim with Chase, so I can't vouch one way or the other. Others, if you search, have mixed success with Credit Card Insurance (One might wonder if you get what you pay for it), so consider the risks.

I do use a Premium coverage through my American Express, I pay a fee per rental to use it, but coverage is much more comprehensive. I have also, in places I have a concern that risk of damage might be greater (I suppose driving on the wrong side of the road with a manual transmission might qualify) just taken the 100% CDW from the rental agency...if for no other reason than peace of mind.

If you google Chase Auto Rental Collision Damage Waiver, you'll find a benefit review of the rental car coverage supplied by your card. Be sure and read this closely (I'd print it out and take it with me). I believe that, for this benefit, you need to decline insurance offered by the car rental agency. (I'm sorry I don't know how to insert a link).

I agree with previous comments in this thread that you need to confirm what type of coverage is provided by your credit card firm. Rental car coverage provided by credit cards is often (usually?) issued by a third party, and the terms and conditions can be extensive. Be sure you're clear on which terms you have to accept on the rental form and which to decline.

read the fine print on what your credit card is providing (Collision?, liability?, Tires,Glass?)

Credit Card insurance never provides liability coverage. The car will automatically come with this.

I do use a Premium coverage through my American Express, I pay a fee per rental to use it

I used to use this but it became a pain. Some rentals like AutoEurope will not process like a rental and trigger the insurance, so you need to call ahead and request to pay the $20 in advance, have it charged to your card as a separate line item. Then additional charges can come through after returning the car, like tolls or one way fee, then you get dinged for a second $20 charge and have to call to have the second charge removed, first the Green Bay Insurance office, "you have to call Amex credit to contest a charge," then call Amex, "No, you have to call the insurance office in Green Bay," then call back to the first place and explain it all again. I've done that circus twice. Then there are countries that Amex doesn't cover. Chase Visa covers all countries. But it doesn't cover theft from vehicle or medical charges like the Amex premium does.