Just as an anecdote, I was Stateside doing my MEP Rating last month.
During our last touch and go of the day at the training airfield, we decided to do a simulated single engine go around at 500' - and see how far it took to reach 1000' whilst enroute to our home airport - this was in a PA-44, set at zero thrust, at blue line speed, 2 POB and with less than 1/2 tank of 100LL, cowl flaps closed, clean configuration, 5 deg of bank towards the live engine and the rubber trimmed out. It took 10.5 nm!
Thankfully, this was a simulation, over the Florida swamps, not a real engine failure in Colorado! Or Surrey! Sobering stuff.