Her option now, with a Charge Certificate apparently served, (although not received), is to wait until the council register the debt at the Traffic Enforcement Centre. When they do this, they will send her an Order for Recovery, and add £10 to the CC amount. The £10 is the TEC registration fee. You can therefore check when they have done this by going onto their website to see when the amount increases by £10. Of course, she should receive the paper OfR by post, but her mail does seem to be going astray. Are you absolutely sure she hasn't changed address since the contravention date ? It might be worth checking with the council what address they are using.
When the debt is registered, she can submit a Statutory Declaration that she submitted representations, but did not receive a notice of rejection. The matter will then be reverted to the "reps" stage, and the council must ask the adjudicator at London Tribunals what they must now do. So don't cough-up yet.