Private life (20 years route) refusal

[Hiro123$]

Sent out an application after having completed the 20 years period (lawful and unlawful/overstaying) required to lodge an application under the 'right to private life' route. Received a letter yesterday informing the request was refused on the basis that I haven't completed 20 years of living in the UK. However, in this period, I only left the country once for 2 weeks to attend my mother's funeral (had a student visa then).

The application included thoroughly evidence of continuous living and included, amongst others:
- the Home Office file showing, for instance, the first date of entry
- 18 years of tax records
- proof of employment letters
- school qualifications
- my child birth certificate (she is 3 years old)
- letter from friends, former work colleagues, my partner of 14 years and mother of my child and vicar from local parish we attend

Additionally, I never used any form of deception to seek and maintain employment. I haven't worked since August 2017 as my employer at the time then requested proof of right to live and work in the UK. My partner's income has been enough to cover our expenses (she is a Brazilian national under Tier 2 visa).

The most striking flaw in the HO decision is that in paragraph 4 of the letter it is noted that I first entered the United Kingdom on 31 October 2000 and that this date has been used in paragraph 15 of the letter to assert that I have not lived in the UK for 20 years (as required under paragraph 276ADE (1) (ii) of the UK Immigration Rules).   This is quite surprising when it is a matter of record on the Home Office file and endorsements in my old passport that I came to the UK with an Entry Clearance on 28 September 1998 and that my leave to remain was extended by the Home Office on 24 August 1999.

There are other sweeping incorrect assumptions in the letter too.

I wonder if anyone has faced similar challenge and if an administrative review of the decision may be a faster and less risky course of action to follow rather than going straight to appeal. Heard/read that the latter can be very lengthy.

Many thanks.