Scam email or genuine?

Just so you know, I am aware of the scam call pretending to be home office. But this is a bit over the top. Anybody has any advice? Read on...

First had a call to advise they need to talk about my appointment. - no action from my part.

Subsequent calls keep saying I need my appointment rescheduled. - I still ignored.

Email came through from seemingly an official domain (..@homeoffice.gsi.gov.uk) to advise as follows:

Dear Sir,

I have been trying to contact you by telephone for the last week to advise you that the premium appointment booked for 15 August at Solihull Premium Service Centre will need to be rescheduled.

Please can you contact me directly at your earliest convenience to arrange this.

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The email signature contains a name, a direct line that starts with 0208 .

This seems pretty genuine but when I log into my premium service booking account it says all okay and my booking status being active. There is a reschedule button which says if I decides to reschedule it will cost me £100 more.

Our booking is on a Saturday. I wonder if it's genuine or not genuine? I haven't returned the call yet.

Seems genuine. Called customer support to check if the name exists on their official staff directory. After confirmation called the lady and she didn't ask for any personal details - just rescheduled my appointment as the are close on Saturday and we booked on Saturday. She said that was an admin error.

So, new booking day is 14th of Aug.