The state pension is already means tested. It is taxable income.
The age related personal allowance has been frozen at £10,500 or so until the standard personal allowance catches up.
Someone with a good SERPS contribution record will get a state pension of almost that anyway, as serps etc is added on top of the basic state pension
In addition, if you get a state pension and have an "adjusted income" of over £26,100 pa, as you might with a public service or private sector final salary pension after decent length of service, the personal allowance is progressively reduced until you are on the standard personal allowance.