Managed to sort out flash on the laptop. It's quite a slow old machine, certainly a lot slower than the desktop on which I'm doing the first set of tests.Neither is young. THe desktop is only a Quad Intel CPU Q6600 at 2.4GHz with 3GB of RAM but it always feels fast and responsive.
Anyway, with flash on the laptop the alternate speed test gives 37.7Mb/s on both download tests and 18.5 up.
Conclusion: There's something odd about the way my main desktop is handling multiple simultaneous downloads. Or possibly with FIrefox, though I'm using Firefox on both machines.