What career/field/job in the UK that doesn't require a degree to start working your way up?

Politics

To work your way up? if you start your own business, a degree is not required, but is still highly recommended. In many jobs, you will find ceilings, that you cannot rise above, without proper education in that line of work, or just a 4 year or higher level. Pay rates also vary more when you don't have the education, but all of your peers or competition for a future position do have. It is easier to get that education while you are younger, and before life happens and gets in your way of progressing or having the time to devote to studying, training or learning.

Building trades are one major exception here. Auto Mechanic, Plumber, Carpenter, Mason / concrete, Metal worker - Welder, general contractor - for the most part can be taught in a trade or vocational school, community college - and the remainder is learned on the job.

Hmmm, must be a muslim trying to find his way into the modern world. Take what you get pal.

Many large businesses in the UK are now taking on Apprentices These include the large banks and financial institutions.

Google the National Apprenticeship Site and
Not going to Uni.

Sales.