I've done work as a contractor through agencies which used umbrella companies. Far from being tax avoidance, some agencies use them as the only way to get paid for the contracting and most of the umbrella companies used make you go paye through them in order to comply with IR35. Then they take a fee for processing and pay the employers N.I contribution from the money the contractor earned. Its a sure fire way of not making as much as you should from a job with a decent rate. A lot of deductions to consider.
The higher quote will probably be from an umbrella company processing on a self employed or Ltd basis and will require A UTR number. That method means you need to fill in a tax self assessment and if Ltd, the tax return for the company.