If I run your speed test, I am told that my average download speed is about 2.4Mbps, which is what BT offer at my address (and which agrees with BT's own tester). The max. burst speed (HTTPx6) down is shown as 3.43. However, while that test was running, tbbmeter showed bursts at about 14Mbps (the scale on the left having changed to max 16).
Also, although my line will provide only about 2.5, when I was downloading an application recently, the tbbmeter scale changed to 32 max., showed quite a long period at about 14 and a burst of about 20.
Can you explain how these high speeds are possible on a line that nominally provides only 2.5 and why your (and BT's) test give much lower rates than tbbmeter?
I have screenshots but don't know how to send them to you.
I might add that the speed shown on tbbmeter has increased greatly since I complained to BT (though the speed test result has not).