Lauren Laverne, the presenter of Desert Island Discs, has said she has been given the “all clear” after undergoing treatment for cancer.

Writing on Instagram on Sunday, the 46-year-old said she would be “back to work” on BBC One’s The One Show on Tuesday after “taking some time off to get better” and thanked the medical staff who had helped her, as well as everyone who had sent her messages of support.

Posting a picture of herself wearing a bright blue sweater with the words “Life is Beautiful” across it, Laverne wrote: “I want to say a huge thank you to the brilliant medical teams who took such great care of me, to the thousands of people who sent me such beautiful and encouraging messages, the friends and acquaintances who took the time to support me after going through cancer themselves – and most of all to my family: my two outstanding kids and especially my husband, Graeme, who was absolutely extraordinary throughout.”

She also confirmed she had been working on new episodes of Desert Island Discs and would be back on BBC Radio 6 Music in the new year. She last presented her 6 Music show on 15 August, with DJs including Nick Grimshaw, Nemone Metaxas and Deb Grant filling in.

The broadcaster revealed she had been diagnosed with cancer in a post on Instagram in August, saying the disease had been diagnosed early and she was expected to fully recover.

On Sunday she said she had been through a difficult time but the experience had “taught me so much about what really matters”.

She added: “I can’t say I suddenly regretted never having hiked the Inca Trail, more that I now see more beauty in ordinary things than I could have imagined, and feel more than ever that the small things in life – the connections we make and care we take with each other – are the big things really.”

A BBC spokesperson said earlier in November: “We’re delighted to welcome Lauren back to the studio this month for The One Show and Desert Island Discs, with new episodes airing on Radio 4 from 1 December, and we look forward to welcoming Lauren back to BBC Radio 6 Music in the new year.”