Maybe not. The ICO says that
The right of access enables individuals to obtain their personal data rather than giving them a right to see copies of documents containing their personal data.
It might be valid to interpret the DPA / UKGDPR in a way that the relevant personal data undergoing processing in their system is the existence of the letters, but that you are not entitled to a copy of the letters. This is in line with the purpose of the right to access, that you can check what data they are processing about you and whether it is correct. If that argument holds and the data subject insists on receiving a copy of the letters, it might be legitimate to charge them a fee for these copies.
But in practice:
- The data controller might not make this argument and just hand over the copies. It is worth a try.
- A right to access founded in data protection might not be the only way to receive a copy of these materials. If the letters are relevant for legal proceedings, they could perhaps be requested during the disclosure process.