If you dont have a bike bag, or know someone who has one which you can borrow, then a spare bike box from the local bike shop should be enough. Shops which I would try would be, Evans, Alpine Bikes, Dales, any other local bike shop, yadda yadda... You'll also need a supply of parcel tape which you'll get from Tesco, Asda etc for about £1 per roll.
The box should be big enough for you to leave your rear wheel on. So, front wheel off, stem off (leave your bars on the stem and put the top cap back on the forks so as to hold on your headset bits and head set stackers/spacers on)
If you had a tensioner, which I know you dont, then I would have advised taking off the tensioner and havng the chain slack, as these can be bashed in transit and end up bending your hanger.
You'll also need to take your pedals off to fit the bike in the box. With pedals, if you have a heavy duty plastic bag or some sort of bag which you can use to keep your pedals from falling around inside the box and scratching your frame and parts, then use that! Pedal pins poke through shitty thin bags.
Best remember to transport a small bag of tools to build up your bike when you get to where you're going! Take that spare parcel tape with you too in a seperate bag.
I usually write my address and contact details on the box too, so if it goes missing or gets mixed up with flights, it can be retured to you.
I've seen people attaching skate boards to the bottom of bike boxes to roll them along instead of carrying them, so if you're overly keen, you could try that too?