If you want to step wise improve a non premium kit beer, where everything you need is not supplied, you will get far more noticeable results compared to changing the yeast by a dry hop or a hop tea to put back some of the flavours and aroma lost in the manufacturing process or to introduce new flavours, with perhaps a grain steep to further improve the beer. You can also do a minimash with grain. If you do any of these things rather than just using an alternative yeast arguably with little or minimal impact, you will find out much more about the brewing process and how ingredients can affect a beer and that will help you make you own informed decisions about what you can achieve.
As for your John Bull kit I suggest a simple dry hop or hop tea with say EKG or Styrian Goldings compatible with the style, or perhaps a citrussy hop like Cascade if you like that sort of thing, backed up with a crystal malt grain steep.
More here
A Newbies Guide to Dry Hopping Your Beer - The HomeBrew Forum
Simple kit plus mini-mash method to improve a kit - The HomeBrew Forum