Buying a new phone and transferring from sim to E sim and keeping my original number.

Hi, I live in the UK and have an old iPhone XS Max with a sim.

My daughter is travelling to the US and is hoping to buy me an iPhone 14 pro max whist she is there.

When she comes back to the UK will I be able to go to an E sim provider like 3 or EE, transfer my old sim, number and data from one phone to the other new phone which uses E sim ? (My current provider GiffGaff does not provide E sim at present).

Is this a simple and straight forward process?

Thanks in advance.