How can I get rid of spiders webs?
Hit them with a sword and you'll be rid of them in no time!
It is also possible to use shears to cut through the web.
You can mine cobwebs relatively quickly with Shears or a Sword (at double durability cost of course), which drops some string.
Also, as you have noticed, liquids like lava work, however I would recommend water over lava because it spreads faster, drains faster when you pick it up again, and, well, it won't kill you.