Not exactly a pub but..... Hops Cellar-www.ballsbrothers.co.uk -
I'm not connected by the way - in fact I'm making my own Cock-a-leekie Soup ,Haggis wi' tatties and neeps for the special night! Followed of course by a wee dram(or two!)
Not in SE1, but W2: if you fancy a bit of Haggis, a few wild reels from the band, a skirl from the piper and a bit o' Burns, try the Rob Roy in Sale Place, W2, 020-7262-6403. Its all free, 8pm onwards (very approximately). Probably the only SE1 connection is that I'm playing. We used to play at the Scotia when it was still Scottish.