It is fine to keep working past your State Retirement Age unless your employment is subject to retirement at a compulsory retirement age.
If your employer does this, they must give a good reason, for example: the job requires certain physical abilities (e.g. in the construction industry) or the job has an age limit set by law (e.g. the fire service).
To be clear, a forced retirement age of 65 no longer exists.
You can also ask your employer if you can work more flexibly or work part-time. They have the right to reject your request.
You can claim your State pension while you are working, as long as you’ve reached the State Pension age. You can also work if you are claiming a personal or workplace pension. However, check with your pension provider or employer if you have a workplace pension as reducing your working hours could affect how much pension you will receive. You should also check to see what happens to your workplace pension if you continue working beyond the age when you can take it.
If you delay (defer) taking your State Pension, you will get larger weekly payments when you do start taking your pension.
You don’t pay National Insurance if you work past State Pension age.