OK, for £200 tops you're a little short of some decent entry level, but not crap bikes, maybe £250 would give you a betterstart, with something that will be enjoyable to ride, and not too heavy.
Search for BTwin, Carrera, and some others which have been mentioned. these will be new bikes.
I've just looked at
ebay, and there are a couple or more for less than £200 which are fairly new, although I'm not sure how close they are to you, but it is worth travelling a short distance to get what you want, and that's really the sticking point - if you aren't sure yet, do some research - it seems your close to something flat bar, and no suspension....
Train are not difficult to get on with a bike, just keep out of peak travelling times.
I have a Carrera Subway 1, 22 inch frame, and it's brilliant, my OH has the 16" womesn frame, and she loves it too, , which will allow us to do a London to Paris, and I cycle a lot around the local area, just for enjoyment, it's simple, and very sood value, but there are others around....
Just keep looking, and ask more specific questions here for guidance, we are really a very helpful bunch!
http://www.ebay.co.uk/itm/Carrera-S...the-goodies-/171883507093?hash=item28050e2d95 just one example...
