If you don't like the idea of London, and don't want to go further north than Leicester, then your options for big cities are limited probably to Birmingham, and maybe Bristol.
Job prospects really depend on your line of work. For example, if you're something like a doctor or teacher, you can probably find work almost anywhere.
For some other kinds of work - for example, investment banking, other more specialised financial work and all the related jobs that feed off them, the
UK is still very much a one-city state, and that city is London.
There are plenty of other smaller cities and large towns in southern England and the midlands, e.g. Southampton, Reading, Coventry, Milton Keynes. To be honest, I wouldn't recommend any of them as a place to look for work on spec - you might be lucky, but you're more likely to be lucky somewhere bigger. And sorry to tell you, you're most likely to be lucky in London, despite the extra expense of living there!