Even by the standards of UK Government the software and support systems behind this are ill-conceived and poorly executed, so don't be surprised if you have trouble using the system or can see glaring holes in the implementation. If this really is a serious attempt by the Government to canvas public opinion, registered voters could be given a cryptographic token to use with this system, making it possible to automatically audit the signatures for veracity and give some confidence Michael Mouse isn't at work in a variety of rôles.
As for the above-mentioned petition, the full wording includes the requirement to pass various tests - it actually places more statutory roadblocks against bearing arms for self-defence than exist currently. The framers of the petition are clearly ignorant of the details of what was actually required to get CCW laws to work for the people in the various States of the US (see, for instance, "CCWs Come With Strings Attached").
In the UK there's no theoretical legal impediment to getting a licence for a handgun for self-defence right now. But in practise they're always refused in the case of common people. There's no theoretical legal problem if you shoot someone in self defence (after all CO19 get away with using it as an excuse for shooting people all the time).
As I've said many times, these kind of people are very much part of the problem, likely a very large part. Tossers. Now the country has gone to the considerable trouble and expense of banning "small weapons" what other possible reason could there be for un-banning them but for RKBA? The point of shooting at targets is to enable you to be more effective when you are forced to shoot at people. It happens to fun too (by which I mean, of course, the shooting at targets part).
Certainly the Government, and the Police, are supposed to be our servants, not the other way around. They've been given (in point of fact taken at gunpoint under the colour of the law) huge amounts of money and, even worse, police state powers yet they've totally failed to deliver the security the people of this country quite rightly expect. They have absolutely no basis for claiming to have a say in this matter. Any moral authority the Government, or the Police, had was squandered long ago.
It is long past time to stop denying this basic human right.
It's plain to me that fundamental human rights, such as the right to keep and bear arms, freedom of speech, to peaceably assemble, freedom of association, habeas corpus, fair and open trial - to name but the most basic, should not be subject to the whims and machination of the democratic and political processes. Sadly Magna Carta, and the spirit behind it, is long dead in the UK. Nowadays the political classes appear to have convinced everyone that we only have entitlements by grace of government, human rights have been effectively abolished by redefinition.
Governments can only deny people their human rights, a government can't give you things it does not, can not, own.
For what I think is "the way" see, Gun Law for the 21st Century. http://dvc.org.uk/dunblane/gunlaw.html