You can't legally represent someone without being authorised or exempt under sections 18 and 19 of the Legal Services Act 2007:
This is because both the "right of audience" and the "conduct of litigation" is a reserved legal activity under section 12 of the Act:
(1) In this Act “reserved legal activity” means—
(a) the exercise of a right of audience;
(b) the conduct of litigation;
(c) reserved instrument activities;
(d) probate activities;
(e) notarial activities;
(f) the administration of oaths.
It is an offence under section 14 of the Act to carry out any of the above, as well as being an offence under section 17 to pretend to be entitled. Furthermore, anyone professing to be entitled to conduct litigation when not so entitled would also be in contempt of court.
However, you may provide the following services without qualification:
(i) the provision of legal advice or assistance in connection with the application of the law or with any form of resolution of legal disputes;
(ii) the provision of representation in connection with any matter concerning the application of the law or any form of resolution of legal disputes.
as these are not reserved legal activities and are not regulated by the Act. So, you could provide a template letter for the person to write and send off their own letter before action, but you wouldn't be allowed to send it on their behalf.
This is because, arguably, letters before action are part of the expected pre-action protocol under the Civil Procedure Rules and therefore constitute part of the conduct of litigation as they are issued as an ancillary function and indeed clause c of Schedule 2, part 4 of the Act covers such ancillary functions:
The “conduct of litigation” means—
(a) the issuing of proceedings before any court in England and Wales,
(b) the commencement, prosecution and defence of such proceedings, and
(c) the performance of any ancillary functions in relation to such proceedings (such as entering appearances to actions).
Therefore, you cannot send the letter on behalf of Alice and you cannot represent to be a solicitor, barrister, lawyer, etc. at any point on your website or in your communications with anybody.