All of the below based upon the fact I've never seen you perform so I am going to presume that you are competent if not totally slick etc etc etc.
I am going to completely disagree with the do it for free route.
I don't perform magic or mentalism in any paid sense although some of my clients get various effects added into what I'm doing for them but that is by the by.
In a 'former life' I provided a much such after lecture service. Initially I provided it on an expenses only basis as I wanted to get the message out and also really loved what I was doing. There was a steady demand. As soon as I started upping the rate - at 18 I was demanding a minimum of £50 an hour (that was <cough> years ago when that would have been more than those on Income Support would get per week. That is not how I worked out the rate; just trying to show that it was not a massive amount but still significant). My bookings soared! People will pay for what they want or need and they perceive quality as reflected in the price. In my case the service I provide one week for some petrol money and a drink was exactly the same as the following week when I demanded the higher amount.
If people don't want to pay or feel it is out of their range they usually won't pay. Some will (they are the ones salesmen love so much). You get a choice to make when someone tells you that your fee is too high. You either stick to your guns or compromise. Quite a few people will meet your demand if they want or made to want your services enough. I'll provide a course in marketing and sales techniques later.

What Magicdicoman has suggested is probably what I would say to you. Quote them a price you know is higher than you are actually prepared to work for. They may surprise you and accept that (especially if they have done any homework and know how much an entertainer costs) or may come back with the more usual, "that's more than I thought/can afford" which may be honest or not. A possible for you is to then ask them what they thought would be a fair rate given the (list) things you are able to do and the benefit to their function. Then keep quiet and wait for them to break the silence. You can smile etc but wait for them to reply. Now you have a decsion to make - to accept their offer as is; to accept their offer but add that you will need your travel expenses and food to be added or for you to accept but say that as you would be doing them such a favour you would noty be able to justify the full routine or two hours or whatever. ie If they don't pay full rate they will still be able to get you but it will be a correspondingly cut down performance. What you never do is work for nothing as that effectively means you are subsidising them and saying that you and your skills are worthless.
Minimum wage for someone your age is about £3.45 hr at the moment and that is for unskilled work. You should be looking at charging at least double that as a skilled performer. Up to you whether that is inclusive or exclusive of your proveable or agreed expenses. Even if your parents drive you to and from the venue there is still fuel costs at least to be covered (even if your parents don't hassle you for it, it is nice to at least offer). Fortunately, at your age there is no tax or NI etc to consider and cash is cash.
Exactly how much you are worth is really for you to decide but if you were upset or disappointed with the £6 per hr you have just received you may want to look towards £10 hr. If you can justify it and find people to pay it, go for it. If you only do one booking at £20 an hour it is the same as four at just a fiver. As you are just starting out I'd recommend going for a larger number of gigs at first just to get your name known but only accept the lower rates on condition that the event organiser does not reveal that you've arranged "a very special rate, just for them".
Quite a few people in the charity business make a lot of money my claiming exaggerated expenses, taking a cut on the take etc. Something I really do not agree with. It is however perfectly fair for you to request at least something towards your legitimate costs eg travel, replacement of expendable props used etc. There are a selection of charities I support and I have arrangements with them whereby I provide my time free of charge and (because I am a supporter) I donate back my expenses (NEVER a "fee" re charities) but in return they agree to my using their name in my future promotional work; which actually promotes them too!!! (We both win). Bottom line is that they are going to benefit from your skills so you should not be out of pocket or under-sell yourself.
As mentioned, ensure you have loads of cards to hand out to people or at the very least include a little sales/self promotion in your patter. This is also a great way to increase your exposure and gain free publicity. I know the media in your home area quite well and there is potentially a lot of mileage to made if approached correctly to promote you and the charity. The secret is in the detail but what may at first appear to be a quite small event can be made much of. Consider why so many 'stars' do so much charity work. Many are doing it for all the right reasons but they also know it won't do any harm to their public profile.
In summary. Decide what you believe you are worth. A little research will uncover what similar entertainers in your area are charging and you can then pitch against that. Always ensure you at least get your expenses and you feel the fee reflects what you are providing - if you under or over price it will do your performance no good as you need to be happy with the situation.. It really does not matter if you are a low cost or a high cost act so long as you are happy with your lot. Other performers in your area may not be happy if you undercut them and thereby do them out of work but that is another story. Do not take that just because of your ager you have to be cheap. It's the entertainment value you are selling, not your age or number of yeas in the business. With charities, be selective and ensure they don't abuse your willingness to help them; offer them big discounts or whatever or even waive all fees & expenses but ensure you demand something in return (even if it is not tangible). If they refuse, so what, there will be many hundreds more wanting something for nothing!!! Don't get yourself an early reputation for being cheap or "that Cozboz will always turn up at minimal notice and do his party tricks". Sometimes a Mothers Union is good to practice something new as they will likely only expect a kid doing some daft tricks and being a small group are prime for experimenting (not as bad as something going wrong in front of a large crowd who've paid a lot to see you) but be warned - they WILL talk about you afterwards and nothing beats word of mouth in advertising & marketing circles.
I hope that lot is of some help to you. No doubt others will knock my attitude of expecting something in return for your time and skills, even if its only to negotiate some shared publicity but I hold strongly to the stance that you should never give your services for free, even if no cash changes hands.
ps Do NOT accept or request tips at a charity event - it will do your image no good at all unless all tips are clearly going direct to the charity.