As I thought, the record is Inverness, Nairn & Lochaber in 1992, won by the Lib Dems on just 26% of the vote in a very close four-way battle with Labour, the SNP and the Tories. The English record appears to be the Portsmouth Central result already given by Al.
There were actually three seats in England in 2010 which were won on lower shares than in Eastleigh: Norwich South (LD 29.4%), Brighton Pavilion (Green 31.3%) and Oldham East & Saddleworth (Labour 31.9%; overturned on petition of course). And there were four more (Great Grimsby, Hampstead & Kilburn, Brum Hall Green, Derby North) where the winning shares weren't much higher.
I thought the point was the lowest by-election margins, so the 1992 and 2010 results you mention do not count...
