I am no expert but did a bit of Googling and here is a summary of what I read:
There are things he can do.
A: Insure his name is on the birth certificate
B: Get Parent Responsibility
Parental Responsibility dictates a parent's legal right to be involved in major decisions regarding the child's upbringing.
C: Legally get a Child Arrangement Order
https://judgelaw.co.uk/children/child-arrangement-orders-for-unmarried-fathers-a-2026-guide/
An existing Child Arrangements Order binds both parents to a specific schedule.
Breach of Court Order: Moving 2.5 hours away will make it physically impossible to stick to the court-ordered routine (such as mid-week visits). If the mother moves without modifying the order, the father can file an enforcement application in court against her for breaching the order.
To make this move legally, the mother either gets the father's written consent to change the court order, or applies to family court to have the order officially varied.
If the mother agrees, both parents can sign an official Parental Responsibility Agreement form. It must be signed and witnessed at a local family court and registered with the Principal Registry of the Family Division. 1, 2, 3]
Court Order:
If the mother refuses the father can apply to a family court for a standalone Parental Responsibility Order using Form C1. The court usually grants this if the father demonstrates commitment and a strong bond with the child. 1, 2, 3]