So, I am applying to join the UK's army. I am an 18 year old male, living in the UK (Obviously.)

However, the problem is, when I was 14, I was diagnosed with later stage cancer - they told me I would die before my birthday, which was 2 months away. This caused me to go into Chemotherapy and, of course, lose my health - rapidly. 

So, I'm currently 18, I finished Chemo at 15, and this year I was told I was in remission. However, I still have the health issues. I am now lazier than I've ever been. 

I want to join the UK's military, because I want to get fitter, but I want to be in shape before joining, so is anyone good with health/fitness, I would appreciate help. 

I don't want to get strong, that's not the goal. I want to be able to run for a fair amount of time, and be healthier.

Currently:
I walk everywhere
I fixed my bike today, so I can start biking more.
I eat a bit at the end of the day, but never before Midday, because I get sick if I do.
My bones are very weak, due to the chemotherapy and cancer.

So is there anyway for me to sort or fix any of this, in a short time?

Running is not a good idea for one with weak bones but I guess what you need is calcium which helps strengthen bones and also you could get Glucosamine which helps re-build joints. I don't think there really is a quick fix for stamina you either have it or you don't. It probably takes months or years of training to improve ones endurance. Yoga may be the way to go as stupid as it sounds, its probably the safest way to get in shape without damaging bones from weight lifting or cardio.

JigSaw : I should have clarified, with "weak bones" I didn't mean they break easily, I mean I can feel really cold in some bones, I have some numbness occasionally. But they don't break or shatter easily, it's probably a muscle thing rather than a bone thing, but I hope that clarifies further.

I'm sorry to say, but I don't think you'll be eligible to enter with having had cancer. Even if you are in remission, I highly doubt you will be able to get a waiver. Knowing what little I know about about our brothers across the pond, I would not get your hopes up too much. 

That being said, start by walking. Once you can handle a few miles, start over with jogging. Work your way up until you can do 2 miles in less than 16 minutes. Try to get to 50 push-ups and 55 or 60 sit ups within 2 minutes without stopping on the sit ups (taking your hands off of your head), or dropping on the push ups (check touches the ground). Figure out what you can handle to start, doing it at least twice a day: when you wake up, before you get into your day too much, and right before you hop into bed. Try to do it more, but don't do more than 4 or 5 sets a day. 

If you can do that, you should be fine by American Army standards for an 18 year old male. 

As for why I'm saying what I am saying the way I am saying, it is because I am a US Army Disabled Veteran, and this is what I did to get myself able to pass my final test in Basic Training. 

thing1 : For the UK army, I am allowed to join, even with a history of Cancer, as long as I can prove that I am in remission and am healthy enough to join, I can join.

I can walk 10KM (6.2 miles) without stopping. I can jog about half a mile without stopping in about 5 minutes, so I'll try to work on that next. 

Thank you, I'm going to start ASAP. It's very much appreciated!

No problem at all. I'm actually surprised that they'll let somebody with a history of cancer join. However, at the same time, I can understand how and why the allow it. 

Honestly,I do not know if you would be able to join. I would suggest visiting a recruiter and asking them if you could with your medical history. They should be able to tell you yes or no quickly. Or look it up on their official web site,that might help you. I would also suggest looking up what your minimum fitness goals in the branch of service you are interested in.

I operate a wellness center so I understand how this works.

Keep with the walking and start adding running. The trick is to spend time on your feet moving, not focusing on the distances. Focus on the time. Say, "I'm going to walk/run for 20 minutes straight." Then go to 30 minutes, and so on. You need to get up to 30 minutes at least if you're going to be physically fit enough to even start military boot camp. It's a grind and the work is difficult. Skip the bike, that won't help, and keep on your feet. If you feel good, try twice a day to go out for 20-30 minutes walking and running. If you can keep running, keep going.

Learn to experience and sustain the discomfort of running. It's not comfortable. It's tough. But you develop some mental toughness as you go and you'll be stronger for the experience after your runs.

Hydrate too. Drink water before you go. There's no other special diet or food you need to eat. Just get out and run one or two times a day, every day.