Tom Bason's side lost at home for the first time since September
Blackheath's recent unbeaten run at home was halted by a resilient Cinderford who beat them 27-18 in National One at Rectory Field.
The Gloucester visitors stood firm against sustained Blackheath pressure to establish a 20-6 half-time lead.
Gravesend maintained their excellent form in London One South with a 17-5 success away to Old Elthamians.
Meanwhile London Two South East leaders Tonbridge Juddians enjoyed a 25-6 win away to Reigatians.
In Kent One, Dartfordians won 24-22 at Cranbrook.
Results - Saturday, 5 December
Blackheath 18-27 Cinderford
National Two South
Barnes 13-23 Canterbury
Westcombe Park 24-28 Ealing
London One South
Dover 27-7 Beckenham
Old Colfeians 62-8 Maidstone
Old Elthamians 5-17 Gravesend
Sidcup 16-12 Chobham
Thanet Wanderers 19-15 Cobham
Tunbridge Wells 6-7 Aylesford Bulls
London Two South East
Bromley 24-0 Eastbourne
Deal & Betteshanger 18-9 Old Dunstonians
Old Reigatian 6-25 Tonbridge Juddian
Sevenoaks 17-9 Warlingham
London Three South East
Charlton Park 10-31 East Grinstead
Folkestone 5-24 Brighton
Hastings & Bexhill 23-12 Old Gravesendians
Medway 28-9 Crowborough
Whitstable 7 Park House 10
Cranbrook 22-24 Dartfordians
Erith 19-11 HSBC
Old Olavians 10-10 Sittingbourne
Sheppey 12-23 Guys' Kings' & St Thomas Hospital
Vigo 24-20 Beecehmians
Bexley 0-56 New Ash Green
Kings College Hospital 24-3 Foots Cray
Lordswood 41-3 Askeans
Orpington 15-5 Old Williamsonians
Shooters Hill 19-0 Brockleians