Yes, reducing white space does degrade the user experience ,The reason being readability of a site is critical in almost all cases and can influence how effectively your users navigate your site. To quote this article about Negative space (also known as white space)
Text on the web is unlike text on any other platform and we all tailor
our designs so the end user has the easiest experience reading our
content. Unlike a newspaper, it can be frustrating on the web to try
and decipher where the content you’re interested in actually is.
Cluttered designs that are too heavy to tackle do not provide a clean,
easy reading experience since we’re forced to scrutinize the web page
first, to distinguish elements from each other. White space hacks a
buffer in between elements, so it’s easier for us to find the content
we care about.
The key thing to note here is the phrase "White space hacks a
buffer in between elements, so it’s easier for us to find the content we care about."
Also the same article has this to say about the impact of white space in conveying a sense of sophistication and comfort to your site making it easier to read:
White space can add a feeling of sophistication and luxury into a
generic webpage by creating the feeling that the product is more
important than the real estate it lives in. It can make a product look
luxurious by using the “less is more” principle. When you look at
Apple’s website – a brand that we regard as being in the more premium
end of computing – there is very little needed, as the products speak
for themselves, albeit alongside some minimalist taglines. This is a
phenomenon that is also popular with premium health and well being
websites where little content is needed to communicate the general
idea of the product or service advertised. Often, cheaper brands
appear to cram as much information into a space as possible; different
markets, different end users. The HP and Apple sites for example,
highlight this point. Apple are notoriously confident and let their
products speak for themselves. If you want the product, have a look
around, if not move along. On the other hand, the HP site employs
busier up- and cross-selling, promoting offers and pushing cheap
pricing into the user’s mind as well as trying to showcase an
assortment of alternative products you could be interested in.
An example of this can be taken from this article (Whitespace: The Underutilized Design Element) which gives an example of Pottery barn which uses a lot of white space to clearly call out its products but also the kind of clientele it serves

However a lower end site on the other hand tries to fit in as much as possible within the screen space as shown by this example of Rooms to Go

I also recommend reading this article about typography which has this to say about the Use of white space and how it influences readability
I also recommend looking at this excellent article about the importance of providing sufficient white space
Since you are designing an Ecommerce site, your primary focus is to drive conversion to your call to action and hence this quote from the above mentioned article is very significant
Whitespace highlights CTAs
Experienced web users tend to ignore banners and, unsurprisingly,
graphic items that look like them. Make links and buttons stand out to
ensure visitors don’t snub them. Whitespace is perfect for this:
Objects and copy framed by empty space are stressed and catch the eyes
of users.
Another interesting thing which is called out in this article how tidiness or a cleaner look actually increases trust due to the professional look it provides
Tidy equals trustworthy
There is a solid link between aesthetics and conversion. A visitor
gauges a website’s professional level based on how it looks at a
glance. Experience adds to this: To veteran users, evaluating a
website’s apparent level of sophistication is second nature and is
done in a flash.
What’s less well known is that ‘appealing’ translates into
‘dependable’, because good web design suggests reliability. Solid
layouts, tantalising images, good colour schemes – all these elements
add to the impression a website makes, but whitespace is especially
important because it indicates expertise. Cluttered designs run the
risk of striking users as cheap and suspect, while plentiful padding
and whitespace signals quality and trustworthiness.
This is important for any website, but it’s crucial for conversion –
an apparently unreliable website sees fewer transactions. In this
sense, less really means more.
Lastly to quickly analyze your site and what the lack of white space does:
- The proximity of the primary call to actions (CTA's) with the same color makes me quickly skim past them without being driven to check them out.
- The fact that your wishlist and your compare use the same background and text as the Add to basket CTA causes the CTA not to stand out and gets lost in all the content that's there.
- Though this concern might not be an issue while using a mouse, I would be have to careful that I dont click the wrong call to action while using a touchscreen device or a smaller form factor due to the proximity of the call to actions.
Other articles to look at :
Designing the Invisible By Luke Wroblewski who says
for designers, white space is often as important as the content
itself,” as such invisible elements of the interface help communicate
„what’s most important, what’s related, and what needs attention.”
Under The Loupe #1: White Space which has this to say
When white space is used appropriately, it allows a page to create a
general flow and balance, which in turn helps communicate the intent
of the design by welcoming readers and inviting them to stay awhile.
White space can highlight important elements and support the overall
hierarchy, leading the viewer around the page by the designer’s
intent. The empty space on a page can be every bit as important as the
space occupied by imagery, because even empty space serves a purpose
and supports the visual integrity of a layout.
Another good resource to look at is 21 Inspiring Examples of White Space in Web Design
Lastly if you are looking for research articles on how white space is useful, I recommend this Pyschology article Reading Online Text: A Comparison of Four White Space Layouts
which has some useful thoughts on how white space influences reading speed and comprehension