You're suggesting that MPs should be able to conduct business in secret in case the tabloid press lie about someone. Have you ever heard the phrase '2 wrongs don't make a right'?

No, he's suggesting that MPs should be able to conduct business in secret because portions of the public have concerns that they have good reason to raise with an MP yet where even the mere knowledge of the basics of the conversation might negatively affect their lives.

E.g. lets say a drug addict who has successfully managed hid their addiction wants to offer their perspective of new drug legislation to their MP. Or a paedophile who wants to gather support for promising treatment option. Or someone with family or community ties to extremists of some shade or the other wants to propose ways of reducing their influence.

There are a multitude of situations where there might be bad fallout from public knowledge about what a persons raises with their MP even if what they raised is positive for the wider community.

Yes, secrecy also allows for negative effects, but it's not nearly as simple as just writing off the benefits of being able to guarantee privacy.

And also if your talking to your mp about the local criminals you might not want the criminals to know that and come round and break your legs.

And of course in NI you might get much worse. As might a moderate reporting problems at a local Mosque

Anonymity does not require secrecy. See Reddit, 4chan, etc: open, anonymous communication.

None of those are anonymous in the face of internet surveillance by entities like the GCHQ or NSA. They are superficially anonymous (or pseudonymous, which isn't the same thing) from the perspective of other users interacting through the intended public interface.

It does if you want people to talk openly, without guarding every word for fear of giving away sufficient detail for someone to be able to identify them. And simply because a lot of people will be unable to trust you if the communication is monitored.

Err this is about a constituant talking to their MP you can not not anonymously lobby and MP

Why not? Lobby your MP, have identifying details removed from the public record. We do it with all sorts of records with confidential or secret details.

Partly because of the rule that MPs are only supposed to deal with their own constituents. Therefore they require your name and address on communications...

No she's stating that there is a long-standing convention that constituents are able to contact their MP in confidence and that this communication should be kept private to protect the constituent rather than the MP.

There's a big difference between the power of a newspaper and the power of a constituent.