* Steel inventory fell to 10.3 mln T last week -Mysteel
* China steel demand to be supported in 2018-2019 -Fitch Solutions
* Top steelmaking city yet to enforce winter cuts (Updates closing prices)
BEIJING, Oct 23 (Reuters) - Shanghai rebar steel futures inched up on Tuesday, buoyed by firm demand ahead of winter when construction usually slows in northern China due to frigid conditions and anti-pollution regulations.
Stockpiles of steel products at Chinese traders fell by 370,000 tonnes to 10.3 million tonnes in the week to Oct. 19, according to data compiled by Mysteel consultancy.
Mysteel said rebar inventory dropped 6.4 percent to 4.12 million tonnes that week, although hot-rolled coil stockpiles grew 0.8 percent to 2.4 million tonnes.
“We think demand in the near-term remains strong, with consumption from the construction sector increasing drastically, which indicates people are working against the clock (before winter),” analysts from Huatai Futures said in a note.
Construction activity typically slows substantially over winter in northern China as freezing conditions close many building sites.
In parts of the north such as smog-prone Beijing-Tianjin-Hebei, building work is also curtailed by rules designed to curb dust over the dry winter months.
The most-active rebar contract on the Shanghai Futures Exchange closed up 0.2 percent at 4,142 yuan ($597.03) a tonne on Tuesday.
Longer term, economic and industry research firm Fitch Solutions expects Chinese demand for steel to remain supported over the rest of the year and into 2019 amid a wave of infrastructure spending.
Prices for steelmaking raw materials were mixed on Tuesday. Dalian iron ore futures for January delivery fell 0.4 percent to 519.5 yuan a tonne.
Dalian coke futures stayed little changed at 2,378 yuan a tonne, while coking coal rose 1.2 percent to 1,388.5 yuan amid tight supply concerns after a coal mine accident in Shandong on Monday that killed three people.
Authorities in Shandong ordered 41 coal mines to halt production for security checks, according to state-owned Xinhua news agency, which would affect coal mining capacity with 89.81 million tonnes per year.
Weekly utilisation rates at blast furnaces in steel mills across the country dipped 0.28 percentage points in the week until Oct. 19 from the week before due to emergency anti-pollution measures in Hebei province, according to Mysteel data. However, rates still reached 68.37 percent.
The top steelmaking city of Tangshan has issued detailed plans for cutting production at individual steel mills, but has not yet instructed producers when to start enforcing the rules. ($1 = 6.9377 Chinese yuan) (Reporting by Muyu Xu and Dominique Patton Editing by Joseph Radford and Subhranshu Sahu)