Afaik, our record unbeaten sequence during PL era was 11 games back in the autumn on 2011.
Apparently there was a 22 game unbeaten sequence in 1949/50 but that was in Div 2, during Arthur Rowe' first season as manager.
Would assume our best top flight run was the Double winners 16 games unbeaten (15 of which were wins) at the start of that glorious campaign.
We were unbeaten in 12 league matches under AVB in 2013.
That 12 match unbeaten run in 2012/13 :
Dec 16,2012 Tottenham 1 - 0 Swansea
Dec 22,2012 Tottenham 0 - 0 Stoke
Dec 26,2012 Aston Villa 0 - 4 Tottenham
Dec 29,2012 Sunderland 1 - 2 Tottenham
Jan 1,2013 Tottenham 3 - 1 Reading
Jan 12,2013 QPR 0 - 0 Tottenham
Jan 20,2013 Tottenham 1 - 1 Manchester United
Jan 30,2013 Norwich 1 - 1 Tottenham
Feb 3,2013 West Bromwich 0 - 1 Tottenham
Feb 9,2013 Tottenham 2 - 1 Saudi Sportswashing Machine
Feb 25,2013 West Ham 2 - 3 Tottenham
Mar 3,2013 Tottenham 2 - 1 Arsenal