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As a Landlord you are under a duty to keep the property in repair. This would include keeping it free from damp. Your tenants would be entitled to serve you with a notice of repair requesting that the damp is removed within a reasonable time (usually 14 days).
If you did not carry out the rent within the reasonable time then the Tenants would be entitled to carry out the repairs at their own cost and then claim the expense from you. They could also get the environmental health department round to take a look at it, they in turn could serve you with an enforcement order.
Until the Tenants serve you with a notice to repair however the above is moot. Reason with the tenants in an attempt to get them to turn the humidifiers on (and keep them on your side) and wait until you have the money to complete the repairs.
Note the tenants can not withhold rent from you in respect of making repair to the damps.
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