If you are a BT customer, and have a BT internet email, you can keep that email address via webmail for free. If you would like advanced features you may be liable for charge from BT. Note, this is something that Ofcom has challenged BT, and we think is rip-off, and another reason to move from BT:
Why do some broadband providers charge for an email address? – Ofcom
We always advise customers to use free email applications like gmail, Hotmail, outlook etc, as those emails are independent of any service provider, and therefore you are free to move to any provider at any time without having any issues for your email address.