I went to unis that were 1 hour away and 5 hours away, so I can opine on both.
If you want independence, all you really need to do is to move out of your house. After that, it depends on how clingy your parents are.
If your parents are clingy, 1 hour away won't make a difference. If they're super clingy, 5 hours won't matter. If you still have your umbilical cord attached, moving abroad for uni won't even phase them.
If they are not at all clingy, moving 5 minutes down the road won't even affect you - I know some people who have not seen their parents in years even though they live 5 minutes walk away.
Do bear in mind, if your parents are super clingy and they can't reach you due to the distance (even if you study on the other side of the planet), they will either:
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Call you all the time (at least weekly)
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Or keep asking you to come home at least monthly (usually weekly)
You won't be able to get away from them due to their nature, not because of the distance.
I once met a girl who lives near the uni (about 30 minute drive) that she attends, but decided to get student accommodation near the uni because she wanted the independence. It worked for her and her parents didn't bugged her about things all the time.
I would prioritise getting into the unis that would give you the best education that you can get over distance from home. It's expensive spending £27k to live independently for 3 years; you will have plenty of time for that after uni.
If you just want to live independently, you could easily get a job now and save yourself studying a degree,
There are also plenty of good universities quite a distance away from ARU, if you can get into them. So it's not like getting a good education and living far from home are mutually exclusive.
By the way are you near Chelmsford, Peterborough, or Cambridge?