The Strictly Come Dancing host says she is not giving up on her marriage.
'The past few weeks have been tough,' she says. 'But we're working through it.'
Tess, 40, resumed her committments yesterday as she went to a north London studio to take part in a photoshoot for her new Marks & Spencer beauty range.
She is also due on The One Show and This Morning next week to promote her book, The Baby Diaries.
'I've been really touched by the support from the public and it feels great being back at work,' Tess tells the Daily Mirror.
On Monday, Tess and Vernon made their first public appearance together since the scandal broke at The Prince's Trust Celebrate Success Awards in London's Leicester Square.
Last month, the Family Fortunes star publicly apologised to his family for sending the saucy messages.
The couple are parents to Phoebe, 5, and 10-month-old Amber.
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- Vernon's text scandal
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