It's a novel idea, that the two greatest Empires in history were directly linked. And it is without doubt that the infrastructure the Romans left behind was very useful for centuries, the A5 road from London to Hollyhead is very much based upon the long straight Roman roads in the area that were linking the capitol to northern citites, especially Wroxter.

However, I doubt that there is a tangible link to the British Empire and how it was built up. Although the roads were used, they were still very often turnpikes and most cargo traveled by ship around the country as it was so much cheaper.

The British Empire was built upon a very strong navy, trading ambition, and ready capital for investment. The Imperialistic culture was not really one that came through the Roman era, as for a large period of time Britain was not as one nation but many kingdoms.

Whereas I am tempted to write a mini essay of my thoughts on this great question, I first point you to a useful essay I ran across as an undergraduate. Manu Lakkur's "The Torch Bearer and the Tutor: Prevalent attitudes towards the Roman Empire in Imperial Britain" is available as a free PDF on Stanford's website. Googling is the quickest way to find it. :) Lakkur has some interesting points you might enjoy reading.

I certainly think the imperialistic culture of Roman colonization influenced the British Empire, but mostly through example as opposed to infrastructure. Rome's colonization of Britain was not, in my personal opinion, its best conquest; therefore, I am not sure the British Empire looked to its own soil for Roman inspiration. :) Admittedly, Rome left Britain with impressive roads, cities, and, of course, London. However, the cultural significance and symbolism of these gems became less Roman and more English over time as the national identity of England developed (though this can obviously be contested). Back to my point - I do not think the British Empire saw itself as inheriting Rome's colonization mission, nor improving its model, but Britain did study Rome's flaws and successes as a way of developing its own empire.