Can't speak for Chelsea but you may pick up Arsenal tickets when they go on general sale, which you might be lucky enough to get when they play a mid-week game against a 'lesser team' - not to be offensive, I mean a team that is in the lower half of the table or one which has just been promoted.

I would be very surprised if tickets for Champions Leagues games would be easy to get for a non member such as the OP, although they could possibly go on general sale but they are more likely to be the seats that cost upwards of £70.