Here's cnlab Speedtest in action:
Left: In theory, up to 3MB of data is transferred for each test - in practice, it's more like 6MB - so bear this in mind if your tariff is tight and you're testing a cellular connection! Right: a test in progress....
Left: the result is in (this time over Wi-fi); Right: all tests are locally and remotely logged, for later retrieval
Left: There's also a buolt in web link to each test device's entries on cnlab's servers, complete with this web form for filtering results and further analysis; Right: you can choose which test server to use, should you suspect that your distance from the current one is slowing things down...