>>>Without your income being affected ie ^^^^ what hours can you legally work
Neither the state pension nor any private pension is in any way 'means tested'. You could be working for 100 hours per week (with billions of pounds in the bank) and still receive both pensions in full.
Anyone born after 5 April 1948 can have income of up to £9440 per year without paying tax on that income. Thereafter they pay tax at 20% on all of their income unless their total income takes them into a higher tax bracket. (Also, if their annual income exceeds £100,000 the £9440 personal allowance starts being reduced by £1 for every additional £2 of income. So, for example, someone with income of £101,000 would lose £500 of their personal allowance, reducing it to £8940).
Anyone born between 6 April 1938 and 5 April 1948 can have income of up to £10,500 per year without paying tax on that income. Thereafter they pay tax at 20% on all of their income unless their total income takes them into a higher tax bracket. However the £10,500 personal allowance starts getting reduced once total income exceeds £26,100, effectively adding to the tax burden. (The calculation is as above i.e. £1 is deducted from the personal allowance for every £2 of income above £26,100. So someone with income of £26,600 would lose £250 off their personal allowance, taking it down to £10,250)
For anyone born before 6 April 1938 the situation is basically the same but the personal allowance figure is £10,660.
Anyone who has reached state retirement age does not have to pay National Insurance (but they do need to complete an exemption form in order to prevent it being deducted from their pay).