The Grenfell Tower fire represents “everything that is unequal and wrong about this country,” Jeremy Corbyn said, as he visited the site on the first anniversary of the tragedy.

The Labour leader arrived at the foot of the west London block to pay his respects, joined by the shadow home secretary, Diane Abbott.

Wearing a green fabric sash around his neck as a sign of solidarity, he greeted and hugged residents before writing a message on the tower’s perimeter fence.

It read: “Love and sympathy to all at Grenfell. Together we mourn. Together we overcome.”

Wreaths and flowers had been piled at the wall after a memorial service was hosted there earlier in the day.

Mr Corbyn had planned to join the evening’s silent march organised by bereaved families and relatives.

Asked what assurances he could give that he was not simply in the area for a photo opportunity, he said: “I have done everything I can and I will continue to do everything I can. I understand the questioning of the role of politicians – that is what a democracy is about – we are here to serve people.”

He added: “I have been here many times in the last year, had many discussions with the families, friends and support organisations – I have come here to show my support, my solidarity, my sympathy, my love for the people that have suffered in Grenfell.”

The Labour leader reflected on his first trip to Grenfell Tower on the day of the fire.

He spoke of meeting “utterly exhausted” fire, police and ambulance crews and paid tribute to the reaction of the local community, saying: “We owe them a massive thanks.”

Describing what the disaster now represented to him, he said: “Everything that is unequal and wrong about this country. This is the richest borough in Britain and the most deprived borough in Britain – Golborne ward is one of the poorest borough wards anywhere in Britain, in the richest borough in Britain.

“Somewhere along the line all those families who have not yet been rehoused, when the luxury flats are still springing up all over London – sorry, people come first.”

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Thursday, 14 June, marks the deadline the council set itself to rehouse all those displaced by the deadly inferno.

However, 42 households from the block remain in hotels, while 52 are in temporary accommodation and 83 in permanent new homes. A further 26 are either in serviced apartments or staying with family.

Mr Corbyn continued: “A year on I would have thought everybody who was affected by Grenfell would have been rehoused. Everybody who had an issue about permanent residency in Britain despite suffering in this fire would have been sorted and been allowed to permanently remain.

“That they would have been rehoused in this area within this community, the community that all those people have known and loved, if that’s where they want to stay – I understand that is where virtually all of them do want to stay.

“I would have thought that we would have learnt the very big lesson from Lakanal House as well as Grenfell, that we need sprinkled systems in high-rise buildings, we do need cladding that is safe and we need the design that is safe that prevents the spread of fire rather than encourages it.”