Your prices are far too cheap to sustain a decent income over the long term. Bristol is not a cheap city to live in!
For sake of argument, assuming you work a 40 hour week doing nails, so that's 8 hours a day over 5 days. If you were to pay yourself the minimum wage for adults rate of £6.70 an hour, that works out at £53.60 a day or £268 a week.
Assuming also that out of the £13 charge for gel nails, £4 covers product costs, professional indemnity insurance, room costs (heating/electricity), advertising, tax and national insurance costs etc, so you actually make £9 per set.
You will need to have a bare minimum of 6 gel nails clients every day for five days every week just to earn minimum wage.
Are you mobile and running a car? If so, you will need to take the car running costs plus petrol into account so you would only be earning about £6 per set and therefore would need to have 10 clients a day....
None of this includes building in a cushion for when you are not working such as if you get sick and can't work for a few days or want to take a weeks holiday.
These are very rough figures but you seriously need to think about setting your prices according to how much money you want to earn.
Do you really want the hassle of running your own business if you end up earning less than a NMW job?
Offering cheap nail services isn't sustainable in the long term and will leave your seriously out of pocket.