Cyber Caliphate Army (CCA), a hacking group affiliated to Isis, hit www.addgoogleonline.com registered by Gandani K for Indian tech firm Always Say, which offers search engine optimisation (SEO) services to local clients.
According to vocative.com website, CCA had vowed on messaging app Telegram they would attack Google on Monday.
"We promised to hack Google. Keep the promise inshallah (God willing), expect us today," the group declared.
However, the website claims that a few hours later they had instead defaced the website www.addgoogleonline.com which is completely unrelated to the Silicon Valley based Google.
After it was hacked, the website played an Islamic State (Isis) song in French and displaced the official logo along with a sign saying "Hacked By: CCA".
The CCA's "defacement of the website" was short-lived as yet another hacker group called "n3far1ous" wiped out the Isis message and replaced it with an "Eat this, Isis" message, and a rock tune playing in the background.
The "n3far1ous" message was still on display Thursday.
The CCA allegedly hacked into 35 British websites, which appear to be a random mix of relatively small British businesses, media reports said.
The websites hacked into include a Japanese dance instructor's website, a company selling furniture and laminate flooring and a salon.
Isis hackers allegedly said that the attacks were "A message to David Cameron" as revenge for the killing of British Muslim terrorist Junaid Hussain, who was killed in a US-led air strike last year.
The attacks follow pro-Isis hackers' threats that they would target the founder of Facebook, Mark Zuckerberg, and Twitter's Jack Dorsey for shutting down their social media accounts.
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