Let me start by highlighting that the Home Office works tirelessly to protect the nation and makes millions of decisions each year that profoundly affect peoples' lives, and for the most part it gets these right. Similarly, the public expects the immigration rules approved by Parliament to be enforced as a matter of fairness to those who abide by the rules.
But you are right that recent events have shown that the Home Office needs to give a human face to how it works as well as exercising greater discretion, where and when it is justified. Steps intended to combat illegal migration have had an unintended, and sometimes devastating, impact on people including the Windrush generation, who are here legally, but who have struggled to get the documentation to prove their status.
To ensure that events of this nature do not happen again, the Home Office is conducting a Lessons Learned review, with independent oversight and challenge. The review will seek to draw out how members of the Windrush generation came to be entangled in measures designed for illegal immigrants. The review will consider the experiences of those involved and wider reflections on Home Office culture as a whole.
MPs commonly report concerns raised by their constituents with their consent and at their request. All information passed on to the Home Office is considered on a case-by-case basis and MPs themselves will often not be in a position to form a firm legal view on an individual immigration case which they have passed on to the Home Office at the request of a constituent. However, I suspect constituents-at-large would expect MPs to report what appeared to them to be clear criminality, especially activity linked to organised crime. Like any member of the public, an MP may decide to contact the Home Office to report suspected immigration offences and I believe there may be an expectation from other constituents that MPs report crimes of which they become aware.