This is a rare occasion - Britain at the top of a chart that's measuring something good! I suspect the scope and influence of the empire might be what just pushes us over the top, though I guess that doesn't explain Denmark too well.
I'd also suspect that another reason is that immigration from Britain was never really an issue anywhere at any point in the history, so there was no reason to limit travel rights of British persons. After all, it was always a modern, industrialized country with English-speaking population, and mostly white (which unfortunately mattered in less enlightened times, not even too long ago).
Accurate : 4 or small 5 penal settlements in a vastly empty continent with only a few hundred thousand native inhabitants started the colonies of Australia. The main reasons for convict settlement in Australia were (a) the loss of the USA in the revolutionary war and, as such, the need for new colonial holdings to offset this loss, and (b) the need to establish a permanent settlement on the continent to cement the claim made 18 years earlier by Captain Cook. It's a little known fact that a French expeditionary force also landed in modern-day Sydney the day after the 'first fleet' landed and erected the Union Jack.
Tiny numbers of convicts (164,000) were transported over a 80 year period from 1788. This is against estimates of the England/Wales population of 8.5 million people, and you can see that transportation wasn't really a useful way of reducing the English population - certainly not as such a great expense when execution was just as effective and a whole lot cheaper (and regularly handed out by magistrates)
Also compare the convict numbers to numbers of people arriving for the Gold rush - 370,000 in 1852 alone - and you can see that while Convicts make for a great story, they really aren't a large part of the story.
So the true story of Australia was that it's foundation as a European colony were more to do with establishing new colonies after the loss of the revolutionary war than it was in reducing english population. The shipping of convicts merely met two aims simultaneously : establishing a colony with forced labour and removing the eyesore prison hulks being used as prisons. It didn't meaningfully help in reducing the overpopulation or unemployment in England. That was eventually solved by free immigration in large numbers to both Australia and the USA/Canada.
Bengal. If you count Texas and California, then Hawaii as well.
Of course, if you compare the British to other colonial powers, they also did a significant amount to preserve the local culture, even when assuming sovereign power from the local states.
And this is only number of countries - it doesn't weight them by importance.
So being able to travel to a dozen tiny Caribbean islands offsets not being abke to go visa free to India or china.
Also visa free doesn't mean much - europeans can go to the US without a Visa, you just need to register online in advance, provide all your details and have the airline supply the details of all the other flights you take, your credit card numbers and what kind of meal you had - but no actual visa
I guess the difference is that in one case they have to explicitly allow you in -- by issuing the visa. And in the other case, they have to explicitly not let you in (presumably by stopping you at the airport before boarding?).
The website with the original data is quite confusing, but as far as I understand the UK is only number one since this year. In 2008 and 2009 it was still number 6.
Initially I also thought it must have to do with the empire/commonwealth, but this makes it seem less likely. And yes, why Denmark? It was number one since 2006!
The only explanation I can come up with for Denmark is that we used to do a lot of humanitarian stuff back before we went evil, so there are a lot of countries that likes us.
