How can I explain to New Zealand Immigration that I am not barred re-entry to UK? [closed]

2 months ago, I was refused entry at the UK border due not meeting the General Visitor requirements Section 4.2. I was told I was not banned from re-entry to UK and my refusal letter makes no mention of a re-entry ban. The refusal letter summarises that I am being refused entry because:

I am not satisfied you are a genuine visitor as required by paragraph 4.2

It also states:

You have not sought entry under any other provisions under the immigration rule

There is no mention of a re-entry ban in the letter.

I have now applied for the New Zealand Working Holiday Visa. I was asked to explain my refusal in the UK which I did by describing what happened and sending a scan of my refusal letter as well as my passport.

They replied asking:

Please advise if you have been prohibited from re-entering the UK. We would appreciate if you could provide any supporting document confirming that you have not been banned from entering the UK again within 04 August 2017.

I have already supplied them with the complete refusal letter.

Is there another way I can explain or show that I am not barred re-entry to the UK?