The mayor of London, Sadiq Khan, has called for the Grenfell inquiry to be moved closer to the homes of the survivors and bereaved, warning that continuing with hearings in the city’s legal district could undermine confidence in the process.

The first phase of the inquiry started this week at Holborn Bars, close to the offices of many of the dozens of solicitors and barristers involved. Survivors have complained that it is too far away and that some cannot travel there by London underground because they are suffering from post-traumatic stress disorder related to confined spaces.

Khan attended on Wednesday and afterwards wrote to the inquiry’s chairman, Sir Martin Moore-Bick, urging him to change the venue as soon as possible. He said it should be held somewhere “more accessible for a group of people who have already been through unimaginable trauma”.

Survivors attending this week’s opening sessions in Holborn, seven miles east of Grenfell Tower, have also complained they are not able to attend as much as they would like because of the travel time – up to an hour each way – while they also balance work and childcare.

Grenfell United, a survivors group, has been discussing alternative venues with the London borough of Hammersmith and Fulham, which is closer to Grenfell. The town hall and hotels in the Olympia area are among the venues that have been suggested. The council said it supported moving the inquiry to west London and sources said it was happy to investigate options.

In the letter, Khan told Moore-Bick: “I am extremely concerned that the use of Holborn Bars may preclude the involvement of the families affected or may negatively impact their wellbeing by doing so.”

He said it was vital that survivors and the bereaved were able to attend in person rather than watch the live stream online. He said they had impressed on him how unsuitable Holborn Bars was, citing the travel time, the stress of being in an unfamiliar part of London and difficulties with childcare and other responsibilities.

Two weeks of commemoration hearings were held at a hotel in Kensington before the move to Holborn Bars.

“A survivor has told me they have only coped with the past two weeks by having family and community nearby to support them,” Khan said. “I fear that using Holborn Bars – a venue that would mean that this network could not be close at hand – would mean that they may be unable to attend the evidence hearings.”

Sid-Ali Atmani, who lived on the 15th floor of Grenfell, has told the mayor’s office that many residents cannot use the tube as they have PTSD. He said the attendance by survivors had been poor and the room where the inquiry was taking place was too cramped, stuffy and claustrophobic.

Grenfell United said it wanted the inquiry to be moved to “somewhere that feels like it’s a place for our community. It is a difficult process for us all, so making survivors, bereaved and the community as comfortable as possible is important.”

A spokesperson for the inquiry said it would respond to Khan in due course.

In May the counsel to the inquiry, Richard Millett QC, said more than 150 venues including Olympia, Kensington and Chelsea college and Newcombe House in Notting Hill Gate had been researched, but these locations were unavailable or deemed unsuitable.

“Holborn Bars was and remains the best available option,” he said. “It is large, it is well provisioned enough for the operation of the inquiry and for the accommodation of a reasonable number of those wishing to attend hearings. It has enough rooms to provide on site the facilities that the BSRs [bereaved, survivors and residents] have asked for. It will be available for the length of time that we are likely to require it, and it allows us to be a permanent fixture.”