Blackheath are now third in National League One following their 40-31 defeat away to Cambridge.
Blackheath were 26-3 down at half time, before improving in the second half to no avail.
Westcombe Park won for just the second time this season, 33-22 at struggling Newbury, while Canterbury's game with Dings Crusaders ended in a 30-30 draw.
Tonbridge Juddians' 52-game winning run came to an end, as they were beaten 27-19 at Cobham in London League One.
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