One answer to this is that the lake actually no longer exists. The Somerset levels (between Wells and Glastonbury) are marshland that originally would have been flooded for large parts of the year. Over time, humans have drained the land for use, but one theory is that this is where the Lady of the Lake and her servants hung out.
Also, King Arthur isn't buried anywhere, he is sleeping in The Lady's care until England's direst need shall come when he will wake again.
I visited a place called Dosmarry/Dosmerry Pool not far from Dartmoor and legend has it that this is where Arthur cast Excalibur. Not heard about Glastonbury though, I thought he was taken to Avalon, or am I getting confused?
Glastonbury is where two richly clothed corpses were dug up in the late 13th/early 14th Century that were declared to be Arthur and Guinevere, but I rather suspect that was propaganda on the part of the English King, Edward I, to claim a link back to the last (supposedly) truly British King at a time when he was trying to conquer Wales and Scotland.