Network Rail says pedestrians have complained about rainwater pooling on the staircase steps.
The judge made the comments as he sentenced the Rooney family for modern slavery offences.
Belton House near Grantham is one of the trust's most visited properties.
Pictures show extent of Skegness blaze
Lincolnshire slavery victim 'made to dig own grave'
Notts County continue their sensational form as they stretch their unbeaten run to eight games with a 4-1 win over Lincoln.
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7 ways to explain the Kardashian phenomenon