Fraud, Error and Recovery powers to monitor MPs’ and Lords’ bank accounts.

The powers in the Bill already apply to MPs in the same way as any other person (there isn't a carve out for them in the Bill), so it isn't clear what additional powers you want to add. MPs are already required to declare financial interests, which you can see here https://www.parliament.uk/mps-lords-and-offices/standards-and-financial-interests/parliamentary-commissioner-for-standards/registers-of-interests/register-of-members-financial-interests/ The failure to register a relevant interest could be a breach of the Code of Conduct for Members, which you can read more about here: https://www.parliament.uk/business/publications/commons/hoc-code-of-conduct/