Dappy was fined £800 and ordered to pay a victim surcharge of £80 and costs of £930.
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A group of 19 of the original 1978-1982 cast met to watch the musical's West End comeback starring TV's Miranda Hart.
Fire crews were called to the 66-year-old's flat in Leatherhead, Surrey after the fire spread from the disposable barbecue.
The operation carried out by Westminster City Council led to the seizure of £8,000 worth of cigarettes.