The Crown Prosecution Service (CPS), arguing on behalf of the Indian government, had agreed to the request and the video has since been submitted to the court.
Mallya's defence team had demanded an inspection of the jail cell to ensure it meets the UK's human rights obligations related to extradition proceedings.
The CPS stressed that the Indian government had provided adequate material which rendered the need for an inspection unnecessary, leading to the demand for a video recording to be reviewed by the court.
The judge is also expected to hear the final closing arguments in the case, after which a timeline for her ruling is likely to become clearer.
The extradition trial, which opened at the London court on December 4 last year, is aimed at laying out a prima facie case of fraud against Mallya.
It also seeks to prove there are no "bars to extradition" and that the tycoon is assured a fair trial in India over his now-defunct Kingfisher Airlines' alleged default of over Rs 90 billion in loans from a consortium of Indian banks.
The CPS has argued that the evidence they have presented establishes "dishonesty" on the part of the businessman and that there are no bars to him being extradited from the UK to face Indian courts.
Mallya's defence team has deposed a series of expert witnesses to claim he had no "fraudulent" intentions and that he is unlikely to get a fair trial in India.
In separate legal proceedings, the businessman lost his appeal in the UK's Court of Appeal against a High Court order in favour of 13 Indian banks to recover funds amounting to nearly 1.145 billion pounds.
The High Court order in favour of the State Bank of India (SBI) led consortium had reinforced a worldwide freezing order against Mallya's assets. It was followed by a related enforcement order in June, granting permission to the UK High Court Enforcement Officer to enter Mallya's properties in Hertfordshire, near London, where he has been based since he left India in March 2016.