Cammy Day, leader of Edinburgh City Council and a supporter of the controversial policy, said he supports the lobby pushing for an extension of the live date.
The Scottish Government has legislated that the licensing system should come under the control of local authorities from October 1, with a new system of fees and regulations, having postponed it since March.
The move, aimed at tackling housing shortages and antisocial behavior, has been criticized by industry insiders as unworkable.
It is feared that high costs and concerns about planning permission are behind the fact that few self-catering establishments, from guesthouses to yurts, remain unregistered.
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Council papers this week revealed short-term rental legislation and tourist taxes are expected to see an 80% fall in available self-catering accommodation in tourism.
Louise Dickins, owner of rental company Dickins Edinburgh and director of the Association of Scotland’s Self-Caterers, told BBC Radio Scotland: “Currently, existing hosts in Edinburgh have to apply for planning and licensing by October 1st.
“It costs £3,000 or more for a one-bedroom flat. The Scottish Government is telling absolutely everyone ‘apply, you must apply now’ but does that mean four out of five applicants in Edinburgh are rejected?
“Registration fees are non-refundable.”
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She added: “It’s not just about losing £3,000, but if you get rejected then you may have lost your livelihood, you’ve lost the value of your business as a going concern, a lot of people have worked in those businesses, that That’s right.” Her pride and joy for years.
“The impact goes well beyond Edinburgh. This is a problem that has arisen in Edinburgh, but assuming we have removed 80% of Edinburgh’s self-catering accommodation, the impact on next year’s festival will be huge.”
Mr Day said the 80% was a “worst case scenario”.
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He said: “We are projecting the worst situation that could happen in Edinburgh. We try to balance the needs of people who live in the city and people who also want to visit the city.
“We have had this discussion publicly, we have campaigned for legislation, laws have come into force.
“Only the government can change that. Lobbying to change this date is active and we would be open to discussion with the government as well. October 1st is just around the corner, but only the government can change that.”
The council leader said that of Edinburgh’s 12,000 short-term leases, only 240 had been registered and 111 had been approved, “and the rest are being processed”.
He said: “You’re right, it’s a low turnout, but I understand towards the end of September the industry will be putting in applications for that October date, but if they want to join us in a lobby to apply for an extension, then we will do that.” I would be very happy to have this discussion.”
A recent survey of around 1,270 short-term rental companies conducted by the ASSC revealed that around 60% of operators have not yet taken steps to apply for a licence.