That's probably true. But it's precisely that which brings into question how important a "personal" relationship to constituents actually is; the shared Anglo-American insistence that national representatives should be strongly tied to some narrowly specific locality seems to be a relic of the era in which elections consisted of local elites delegating one of their number to the capital, it really has very little to do with modern mass-democracy. The fact that the US can employ districts so vast and, often, so bizarrely-defined as they do and nobody really seems to notice or care just highlights how archaic that whole logic is.
Expand the House, like Antilogic says, introduce multi-member constituencies (state-wide were necessary, regional where possible), the whole system begins to make a lot more sense.
Indeed. I can't remember the statistic offhand but only something like 10% or fewer of British people can actually name, let alone recognise, their own MP.