What about, say, the South Sea Company?
At its peak in 1720 its shares were trading for £1050 each. So how much was it worth?
Time to do a little calculation!
As far as I can find out, around 3.5 million shares were released, which gives it a peak value of £3.675 billion. But that's in 1720 pounds. There's been a lot of economic movement since then, so what could that be in 2012 pounds?
I found a useful web site, Measuring Worth, that contains the tools for calculating the relative worth of various currencies at various dates.
Using its tools it turns out that the South Sea Company would have been worth at the low end £429 billion in 2012 pounds, but at the high end £49.3 trillion.
Which at a £/$ exchange rate of around 1.5, gives us a top end value of $73.8 trillion.
I think the UK can claim that record then.
It's just a pity about happened next.