The SERC is not so sure:
"City size and diversity, however, provide an economic payoff: a critical mass of people, resources and ideas help produce agglomeration economies
(Glaeser 2011). Increasing that critical mass helps raise productivity, therefore: the consensus
from recent studies is that doubling employment in a city raises average labour productivity by
around six percent, although these effects are much more important for some types of economic
activity(Melo, Graham et al. 2009). They are much more important in precisely those sectors of
economic activity in which the British economy is specialised and our most prosperous cities – the Londons, Cambridges and Oxfords – are particularly specialised: skill intensive traded services.
Although urban density is strongly correlated with the effective or functional size of a city there is no evidence that density itself is a cause of these observed agglomeration economies. It seems more likely that density is the outcome of agglomeration economies as both households and firms bid up the price of land to benefit from them thus causing development to be at higher density. Indeed Cheshire and Magrini (2009) find that once all other factors including city size are controlled for, higher density is associated with slower urban economic growth."
And they have interesting examples:
Two examples illustrate the difficulty of separating out density effects. 1) Building CrossRail, for example, will likely reduce the density of the London region as a whole as people take advantage of quicker travel to
move out to cheaper land. But it will still increase the effective size of London since with easier travel the costs of productive interactions between economic agents will fall and their potential number will increase. 2) Take two cities with identical populations and borders: building more houses will increase density. But it is then hard to attribute any subsequent economic changes to higher density, since population size has also gone up.