Welcome to the forum MH!
I've done the Brubox a few times, and the London Bitter is very good indeed (if you have a search around you'll find that 'nicktherockstar' has also done this one a few weeks back.
Bottling definitely gave me the best results, buts that's probably because that gave me a chance to leave it longer to mature.
The instructions are pretty good. So long as the bubbling in the air trap jar/bottle is down to less than once a minute then you can continue.
1. Put the polypin into its box, tip it up so the tap is on top, expel as much air as possible and close the tap. The fermentation will still be going very slowly and will produce more CO2. You will have to periodically release the pressure (maybe twice a day to begin). As it settles down a bit the beer will begin to get a bit clearer (although its hard to tell in the box!).
2. When you no longer have to release then pressure too often (they say 5 days but a couple of weeks like this won't do any harm) you can bottle it. A day before carefully tip the box back so that the tap is at the front bottom (ooerr missus, 'front bottom'

). This will give the yeast a chance to settle again before you bottle it.
3. On the bottling day, sanitise your bottles (a soak in a weak thin bleach solution or a weak solution of the Bruclean that comes with the kit will do) and rinse them well. Also sanitise a tea spoon and the short length of tubing used during fermentation.
4. Pop 1/2 tspn of sugar into each bottle (granulated is fine, but preferably from a new packet to minimise the chance of any bugs getting into the beer).
5. Put the tubing onto the tap, and start to fill the bottles by placing the tubing to the bottom of the bottle and slowly opening the tap until its almost full.
6. Put the caps on the bottles, gently invert them a couple of times to mix the sugar and keep them in a warm place (about 20 °C) for a week. Then transfer them somewhere cooler for at least another couple of weeks.
I found that it took 4-6 weeks to reach its peak of condition. Painful as it may be, patience really is a virtue here

To help you while away the time why not get another tin and get the next brew on!