[davem]

The large bridge was cut - Tolkien is clear:

The bridge was gone, and his enemies were on an island in deep water too deep and dark and cool for his liking. If he plunged into it, a vapour and a steam would arise enough to cover all the land with a mist for
days; but the lake was mightier than he, it would quench him before he could pass through.

You can't get away from the text. "The bridge was cut & his enemies were on an island" cannot be interpreted in any other way than that the big bridge was cut/thrown down.

As to the picture, it is wrong - in Barrels out of Bond we read:

It seemed a town of Men still throve there, built out on bridges far into the water as a protection against enemies of all sorts, and especially against the dragon of the Mountain. From Laketown the barrels were brought up the Forest River. Often they were just tied together like big rafts and poled or rowed up the stream; sometimes they were loaded on to flat boats.

built out on bridges far into the water[ does not conform to the picture, which shows only one large bridge, & Lake Town is hardly 'far out'. Hence, the picture is both correct & not correct (& possibly so is the text). The only explanation I can think of to this dilemma is that Tolkien at some points visualised Esgaroth as being linked to the shore(s) by a number of bridges which could all be cast down (ie they were some form of suspension bridge) & at other points he conceived of it as having one big, substantial bridge

A great bridge made of wood ran out to where on huge piles made of forest trees was built a busy wooden town, not a town of elves but of Men, who still dared to dwell here under the shadow of the distant dragonmountain.

So, there is a single, great bridge built on huge piles of forest trees, which clearly (from the picture) could not be 'cast down' or cut in short order unless it had some form of mechanism built in (possibly of Elvish design???) & at the same time there are a number of bridges which can be cast down - the book seems to contradict itself. Whatever, Tolkien clearly states that when the Dragon attacks the town is an island in deep water, so whether there was one, or many, is not really the issue.

The only possible way of making the two concepts fit is that lake Town was a collection of seperate buildings connected by bridges - but you still have to accept that the big bridge was destroyed in some way because when Smaug attacked it was cut off: 'an island'.