How long should it take to reach grade 1 piano?

I started having lessons towards the beginning of January this year and I'm doing a prep test in a couple weeks time. I'd like to know how long it could take to reach grade 1; I practise around 3 days a week for around 30 mins (during holidays I practise everyday for 45mins/an hour). My teacher has mentioned a couple of times that I'm progressing well for someone with no prior musical experience but I'm still unsure how long it'll take to do grade 1 (btw I want to do it as soon as possible as gcses are next year and I leave shortly after which means I'll have to find a new teacher).

Any tips/advice is appreciated

Hiyaa, I'm a grade 8 piano player, got the exam on 25th June and then I'm done.
I started off like you, absolutely no prior knowledge. You are doing a good job by keeping regular practise. 1/2 hour is a good amount of time whilst reaching grade 1, however if you want to do higher grades keep in mind you may have to practise longer as material is much hard- I practise 4 hours a day.

I started learning piano at the age of 7 and it took me about a year to reach grade one standard as a was a slow learner- but this varies from person to person.
Just make sure you know your basic theory- like notes and time values, key signatures and time signatures (hopefully you know what I'm talking about)- this should make the learning process quicker for you and you'll be able to progress at a much quicker pace.
To complete a grade, it usually takes a year if you want to achieve good marks.

Hope this helped,
Let me know if you have any questions or help.