There's no need to speculate, there's no dark crystal or sugar in the current Fuller's partigyle, they've tweeted a photo of their actual brewbook :
Burtonise, 7.2% light crystal, splash of chocolate malt and you're good to go. Later in that thread someone has worked out a detailed recipe for ESB, which he claims is close.
As always with British recipes yeast is crucial. WLP002 and 1968 don't have the typical marmalade character of the real Fuller's yeast, apparently Imperial Pub does - or harvest it from bottles of 1845 or IPA/Lancer.
It's not often that you get to compare the actual recipe with other sources that attempt to clone the beer - it's a good test to compare how close your favourite source of clone recipes is.
I've been making ESB and London Pride for a couple of years now. The recipe I used comes from an interview I heard with John Keeling who at the time was the head brewer at Fullers. It differs slightly from the brew log sheet posted in the Twitter posts shared on Homebrewtalk.com but the recipe has evolved and changed over time. Either that or John wasn't telling the interviewer the full truth.
Mr. Keeling stated: 95% pale ale malt and 5% crystal 150. Without re-reading the HBT thread again I believe the hops were the same... Target for bittering, and late additions of Northdown, Challenger (and Golding for dry hopping in ESB). He said 80% of the bitterness comes from the Target and the remaining 20% from the late additions. According to the interview ESB was around 43 IBU and LP 31 IBU.
I've been brewing it this way ever since I heard that interview several years ago but my most recent version, in the fermenter right now, uses the grist from the HBT forum which adds just a bit of chocolate malt. Can't wait to see how it differs.
I'm scouring the notes I made during the interview trying to find out what yeast he said but either he didn't or I didn't write it down. Like Northern_Brewer said I've been using Imperial Pub A09 with good results.