"We don't comment on the detail of individual cases, but can confirm we will offer to speak to Mr Khan about how he should apply for the correct type of visa to do what he wishes to do in the UK," a British High Commission spokesperson said on the refusal of visa to the internationally renowned musician.
The UK Home Office, in London, without giving specific details, said visas are declined due to incomplete information.
The 70-year-old artiste, who was to perform at the Royal Festival Hall on September 17, had said that he was "shocked and appalled" at the rejection of his visa application.
Tagging Foreign Minister Sushma Swaraj in his tweet, Khan had written, "My UK visa rejected. Extremely sad for artists who are spreading the message of love & peace @HCI_London @MEAIndia @UKinIndia @SushmaSwaraj."
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"Shocked and appalled. #UK visa rejected. Scheduled to perform at the #RoyalFestivalHall in Sep @HCI_London @MEAIndia @SushmaSwaraj @UKinIndia," he further wrote.
Expressing disappointment over the denial of the travel document, Amjad's son Amaan Ali said, "This has never happened before...He is someone who has worked all his life for the country and peace. The government should take interest why they (UK) are doing this."
Meanwhile, the longest serving Indian-origin MP Keith Vaz sought an explanation from the UK Home Office over reports of refusal of visa to Khan, saying the decision would "severely damage" Indo-UK relations.
"I am astonished at this news. Amjad Ali Khan is one of India's greatest living artists and I cannot believe that his visa has been refused. I have today written to the Home Office and asked for an explanation and for a reversal of the decision," said Vaz.
"Listen as legendary sarod player Ustad Amjad Ali Khan reflects on his 50-year career. His wife Subhalakshmi Khan joins him for this candid conversation," reads the programme for the centre's 'Classical Season 2016-17' as part of the annual Darbar Festival.
A Southbank Centre statement said, "It is extremely unfortunate that Amjad Ali Khan has been refused a short-term visa to come and perform at Southbank Centre, which we understand is due to a recent change in the visa's guidelines.
"We are working closely to try to rectify this situation and are hopeful that he will be able to perform on September 17 at the Royal Festival Hall as planned," it said.