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The party made the city's cleanliness a top priority in its manifesto at last month's local elections.
In a motion to today's meeting of the full council, group leader Iain Whyte notes other parties also highlighted issues like street cleaning, waste management and recycling during the campaign.
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And he asks for a report from officials on how some of the ideas – from a graffiti task force to scrapping the charge for special uplifts – could be implemented and how much they would cost.
Last year, environment charity Keep Scotland Beautiful recorded a big drop in the proportion of Capital streets considered clean, from 92.9 per cent to just 81.2 per cent – worse than Glasgow.
And city developer Chris Stewart voiced frustration about poor rubbish collection, offensive graffiti and pavements in disrepair, complaining that standards had slipped.
Councillor Whyte said: "I had hoped things were getting better because we kept being told it was because of Covid absences and although we now have an increase in cases that follows a period when things were more back to normal.
"But I've seen tweets about bins in Leith where the amount of dumping around them is horrendous, I regularly see overflowing litter bins still, and there are streets where you can see weeds all along the edge of the pavements."
Other suggestions highlighted in the Tory motion include a well-resourced enforcement team to deal with fly-tipping, dumping around bins, litter and dog fouling; a comprehensive weed clearing programme; an improved maintenance schedule for litter bins; technology solutions for reporting problems, like with QR codes on bins; and re-instating regular clearing of street drains to prevent local flooding.
The Tories also call for the scrapping of the garden waste charge; a review of the controversial bin hubs project; retaining gull-proof sacks where they are wanted in the World Heritage Site unless a better alternative can be implemented with residents’ support; and starting a programme to put communal bins underground wherever possible.
Cllr Whyte continued: "There is something about our systems we have to improve and it may need some more resources, but we really do need to get these basic services right
"The key thing is to get a report back on how we can really achieve changes fairly swiftly the nature of cleanliness in the city and other things that make the place look unkempt like the weeds and, where we can, potholes and surfacing."
Council leader Cammy Day said the budget agreed in February already included provision for a spring clean-up of the city.
He praised council staff for the work they had done during the pandemic.
And he added: "I'm happy that we should receive a report on what we can do to keep the city clean and I've said publicly I want to get the basic services right. And if that's about spending some resources we've agreed in our budget on clearing up the city then we should get on with that."