hey

you'll need to update your existing worker registration certificate since you've started new employment and this is going cost you nothing

 

The WRS is a formality with the UK government only. You being a Polish National, employers are aware that you have a legal right to work and stay here, and meeting the requirements for applying for the EEA1 (you worked 12 months with the WRS), you already have right of free movement. The EEA1 is just proof in your passport of this, though for EU nationals it is not a requirement (Home Office websites even state this).

No need to apply for another WRS. You only do this if within the first 12 months, you were between employers and the gap between is more than 30 days, then yes you have to apply again for the WRS for the new employer.

So for your new employer, no employment proof should have to be given as you now have met the initial 12 months on WRS as required by the UK government. Direct them to the Home Office website if they insist on proof that you can work, as they are just being ignorant at this point.