I invested in a new 24 US gallon tank and as of today have begun a fishless cycle. I was told to check the water weekly (I invested in a master kit) and jot down what the readings are:

PH: 8.5
Ammonia: 0
Nitrate: 0
Nitrite: 0

I've heard that the readings are meant to start high then reduce? Apart from the PH being high, this seems like "ideal" water conditions for my fish, but I don't want to put them in until the cycle is complete! Any suggestions? Should I wait a couple of weeks or put them in now?

What are you using as your source of ammonia? You cycle won't start until you supply the necessary fuel (ammonia) to kick start the colonisation of nitrosomonas in your filter

I haven't put any in, as yet. Mainly because I haven't been able to find any! Where would I get pure ammonia and how much would I put in?

Would dropping one or two flakes of fish food into it help any?

Unfortunately dropping fish food in means it takes a long time to cycle. I tried it this way once and at the 7 week mark, I was still in the ammonia phase and the nitrites were only just starting to rise....

If you can't find any ammonia in store - you can try something that a few friends of mine have and that's to use a few drops of pee (I know, I know - sounds gross but it's pure, clean ammonia ). One friend cycled this way and the tank was ready for fish in 5 weeks - which is a good timeline. He would just add about 4 drops each day and test... he made sure the ammonia would get to 2.0ppm and stay there and then chart when the nitrites kicked in...

I thought it a great idea myself

I've heard that the right ammonia can be hard to get in the UK, so you may not be able to find any.

It is possible to do it using food, but I don't know how much you'd put in.

If you can seed the filter with some squeezings from your current tank, that would help it cycle a lot faster.

I put the plant in from my old tank, which had some algae on it, so I'm assuming that this is going to somewhat give a hand in building the cycle. The pee idea is good, but considering I drink both tea and alcohol (though the latter only once/twice per week, if that) wouldn't this be a bad thing? I'm also on antibiotics... don't want to hurt them by poisoning them with me pee!