Petitions have always been a part of government life, either sent by post or delivered to Number 10 by hand.
The official Number 10 Downing Street website contains, amongst many things, a section for e-petitions. These can cover virtually any subject, and they do. The website states:
You can now both create and sign petitions on this website too, giving you the opportunity to reach a potentially wider audience and to deliver your petition directly to Downing Street.
One recent petition might be of particular interest: We the undersigned petition the Prime Minister to resign.
As of the time of writing, there were 12,750 signatories.