Ok - firstly you should have a letter of engagement which sets out the responsible partner for your work and the firm’s complaints procedure (along with charging procedures). This letter must be sent out, so you should have one. If not, speak to your solicitor and ask, check the website or phone and ask reception for details of the complaints partner.
You must firstly follow the firm’s procedure. If you don’t, you’ll not get very far with other organisations.
If that gets you nowhere, the correct body is the SRA, not the Law Society which ceased dealing with complaints a while ago now. It is the SRA responsible for regulating solicitors.
In terms of costs / quality, your OP is not entirely clear. Are you being charged £309 per letter, or does that include all the work that goes into preparing the letter (including calls/meetings to take your instructions, revising drafts etc) I used to charge £350 + vat an hour in private practice (just for an idea). Whether the costs you’ve quoted are reasonable depends on the nature of the letter, the instructions you‘ve given (was there missing information for example), the level of person writing it and the level of firm (ie high street, specialist or major commercial firm).
Can you give a bit more info ?