First, you have the cheese. "Tradition" would dictate a nice hunk of Cheddar (English, of course) or Stilton. Personally, I'd love a bit of Stinking Bishop as an alternative. Just keep it robust and, above all, keep it English.
Next up, the pickle! No two ways about it, it's a Branston pickle all the way. (For those not in the know, Branston pickle is an English pickle relish.) There seems to be very little wiggle room here, though I did find a few references to using pickled onions in addition (not as a substitute, mind you).
Last, a hunk of bread! Fellow New Yorkers, I completely visualize Sullivan Street's Pan Pugliese in this role. Regardless of what you choose, keep it white, crusty and rustic!
Most recipes I found also included a salad. To me, this seems just a little at odds with the rest of the meal. A hunk of cheddar, a hearty loaf of bread, and… a bed of mesclun greens? It just doesn't sound right. I much prefer the idea of using that stomach space for a pint of beer to wash it all down with!
Though we might be a long way from an English pub, it just takes a bit of cheese and some imagination to get you there. Enjoy!