You need to do the following
Resign formally from your previous club. You need to do this by email or letter and you should keep a record of the date of resignation and ideally a copy of your resignation letter or email.
If possible get written confirmation (email or letter) from an officer of your previous club stating that they have no objection to you changing your First Claim Club.
Log onto your account on the England Athletics myATHLETICS portal using your URN as your username and start the change process using the appropriate menu item.
The portal and the form both say you need to send a cheque for £10 payable to England Athletics. If you were last affiliated more than two full seasons ago then it is worth phoning England Athletics to ask if the fee is applicable.  For example, if you last joined your previous First Claim club in May 2013 and they affiliated you then then your affiliation would have lapsed on 31st March 2014  If you then wanted to change your First Claim Club to Red Rose after 1st April 2016 then two full seasons would have passed and the fee should not be charged.  Phone, put your case to them and hope you are successful.
Applications received by England Athletics are often processed in a few days.  If you want more information on timescales then please contact England Athletics directly.
If you do not hear from England Athletics then phone them to understand why. If you do hear from them then please let the club’s Membership Secretary know. England Athletics sometimes tell us but sometimes they forget. If they forget and you do not tell us then we will not affiliate you.