The former Bond girl and Strictly Come Dancing contestant said on Twitter that the two trees, at the front of her £900,000 Cheltenham property, were "wrong for the area" and that one had been judged unsafe by tree experts. They would be replaced with holm oaks, she added.
One long-time nearby resident said felling of the "iconic" trees would "change the whole atmosphere", while another described it as "vandalism", carried out to "make some cash".
But Cheltenham Borough Council tree officer Lindsey Mulraine said the trees "had reached the end of their useful life", adding: "It's a shame to lose them, but it was felt they were not worthy of a preservation order.
"We did publicise the proposed works and no objections were received."