Were blue-tinted glasses prevalent in Victorian England and, if so, why?

'How common' is a difficult question to answer because I doubt there were any consumer surveys in those days and 'common' is a bit subjective. Judging by the number of references, tinted glasses (also blue) were not unusual but I doubt that there were many users outside of the better off because of the cost. Anyway, here's what I've found that gives some ideas why people had tinted or colored glasses in the past.

Some of the earliest tinted glasses were used by the Chinese.

Dating back about 900 hundred years, Chinese people were known to use flat pieces of smoky quartz as vision aids. Known as Ai Tai, meaning ‘dark clouds covering the Sun’, these types of lenses were incorporated into spectacle frames around the 15th century. They were worn for many purposes which included therapeutic and ceremonial uses. Some historical accounts describe them being worn by court judges to conceal their facial expressions during trials.

Here we have a European reference from the 15th century (and after).

In 1459, the Portuguese scientist Nuno Fernandes imported from Italy one pair of spectacles with colored lenses to use them when riding in the snow. This is probably the first record of someone using a pair of glasses to protect the eyes from the sun’s harmful rays. But for centuries, the function of tinted glasses was mainly therapeutic: many thought that blue or green lenses could correct certain vision impairments.

From the same source as the China reference (the writer maybe isn't aware of the Portuguese gentleman).

The first tinted spectacles intended specifically for sun protection were worn in Venice, Italy in the late 18th century. They were known as Goldoni Glasses, named after the famous playwright Carlo Goldoni who popularised the style. They were most often worn by gondoliers who needed protection while working in the sunny canals of Venice.

Now, this next one is maybe a bit controversial.

Also in the 18th century, therapeutic eye-preservers became popular in Britain for those who suffered from pre-existing conditions that made them sensitive to light. Though not technically considered sunglasses, it was thought that their blue or green lenses would correct vision impairments and alleviate discomfort caused by glare.

The maybe controversial bit is 'pre-existing conditions. This maybe includes sufferers from syphilis. This disease is mentioned on quite a lot of web pages as a reason for wearing blue tinted specs but others say there is no evidence.

Revisited Myth #51: Wearing tinted eyeglasses meant the wearer had syphilis.

Medical books of the time make no mention of colored lenses in treating syphilis. In Treatise of the Venereal Disease (1789), the author notes correctly that syphilis could cause eye inflammation but offers no specific treatment. In his Observations Concerning the Prevention and Cure of the Venereal Disease (1796), William Buchan recommends blistering plasters applied to the temples or behind the ears to reduce some of the symptoms. No primary reference to the connection between colored lenses and syphilis has been found.

Dr.Lindsey Fitzharris has a syphilis archives website and also says there is no evidence (and mentions cost of glasses would be too high for most people).

Next, something on the color blue in Steampunk Glasses With Blue Lenses: Why Is It Such a Good Idea?

In England in 1854, Robert Hunt found that a light beam passing through a blue lens could magnetize the needle of a compass. No other lens color achieved this result. As a consequence, mystical powers were attributed to blue glasses, and they became very popular.

Later, in 1871, American General A. J. Pleasanton demonstrated that the sunlight filtered through dark blue glass stimulates the growth of plants and animals. Many concluded that wearing eyeglasses with blue lenses would be beneficial to the human eye.

According to J. William Rosenthal, these reasons explain why blue spectacles were so widespread in the 19th century. So, choosing steampunk glasses with blue lenses is the way to go if you want to commit to 19th century fashion.

I don't know what the writer here means by 'popular', but there is a reference and google link given to a book called 'Spectacles and Other Vision Aids: A History and Guide to Collecting'.

Tinted glasses became a fashion item as well.

With lens technology and accurate prescriptions becoming ever more affordable during the 1800s, the 1900s saw a trend toward making glasses fashionable and stylish. Frames with different shapes, materials, and colors became available for those who wanted glasses to match their face shape, eye color, or outfit.