State Benefits - Unemployment benefit is taxable

Sickness Benefit and Invalidity Pension are paid on the basis that you are incapable of work because of illness. However, it is possible that you can be allowed to work for therapeutic reasons. If you need to do that, your doctor and, the DWP have to agree beforehand. The work normally has to be very different from any sort of formal employment and must fit in around your illness. You cannot earn more than £297 a week from therapeutic work. If your earnings vary, they must not generally be above £267.

If you have an adult dependant such as a husband or wife, you will get extra sickness benefit or invalidity pension for him or her. That will be stopped if the dependant has earnings (including any pension from their job) of more than £119.80 for sickness benefit or £168.79 for invalidity pension.

Sickness benefit and invalidity pension are not taxable.

Income Support or Housing Benefit If you claim income support or receive housing benefit, your earnings count as income and reduce your benefit. The first £9 a week of earnings (£9 each for a couple) are ignored (and in some cases it can be up to £19 ), but anything above that reduces your income support penny for penny and your housing benefit at the rate of 61/8p a week off your rent rebate and 8p a week off your rates rebate for every 10p a week earned.

Income support paid to someone under pension age is taxable. Housing benefit is not taxable.

More on Working in retirment

State Benefits - Calculating Earnings

Earnings are net earnings after deducting tax and National Insurance. Except for income support and housing benefit, you can also deduct any expenses of working including travel, 4.9 towards a meal, and anything else which is reasonable and incurred because of the work. If you work occasionally or irregularly, your earnings are counted for the period to which they relate. For example, if you do one day's work and get one day's pay, you cannot average the amount out over a longer period.
National Insurance
Everyone under pension age has to pay National Insurance contributions if their earnings exceed £8i a week (this amount changes in April each year).
The contributions are normally 0.09 of earnings up to 609 a week. But since October 2009 people on low incomes . . . ... see: State Benefits - Calculating Earnings