You might be interested in the information on running a limited company which you can find here.
As a rule of thumb, there is more potential for savings of tax and national insurance contributions the higher the level of profit. The compliance costs of running a limited company would probably exceed any savings on a profit of £20,000. Put £20,000 profit into the calculator here to compare the results for a self-employed individual with that of a company director/shareholder. Then try it with a profit of £40,000.
If you are self-employed, you pay tax and NIC on whatever your profit is. You have a personal allowance for 2015/16 of £10,600 and will pay income tax on the next £31,785 at 20%. You then start paying tax at 40%. Class 4 NIC will be charged at 9% on profits between £8,060 and £42,385 and at 2% on the excess over £42,385. Class 2 NIC at £2.80 per week is also payable.
If you operate your business through a limited company, whilst the company itself will pay corporation tax on its profits at 20%, you can choose when and if to take out income in the form of salary and/or dividends which can help you to stay out of the higher personal tax brackets if you wish.
If you take a company salary, you will pay tax on the excess over your personal allowance, £10,600 for 2015/16. National Insurance Contributions will be payable on that part of the salary in excess of £155 per week at 12% by the employee and at 13.8% on that part of the salary in excess of £156 per week by the company. Take a look at section 4 of the notes here.
A salary is a tax deductible expense for a company. As stated above, a company will pay corporation at 20% on its profits so a salary will reduce its tax liability by 20% of the sum of the gross salary and employers' NIC. However, you may have personal tax to pay on at least part of your salary which will reduce the tax saving made by the company.
As a shareholder, you can take dividends from a company so long as it has post tax profits. Dividends are not a tax deductible expense for the company so they will not reduce its corporation tax liability. However, dividends are not subject to NIC and are treated as basic rate tax paid so you will have no personal tax to pay on them if your total income in 2015/16 is £42,385 or less. Take a look here for information on dividends and tax.
You really ought to discuss this with an accountant or tax adviser face to face. At some stage, assuming your turnover increases whether you are self-employed or running a limited company, you will have to look at VAT. In addition, there is the Construction Industry Scheme (CIS) which has fairly onerous compliance procedures which you might feel are better dealt with by an accountant or tax adviser.
I hope this helps but let me know if you have any further questions.