When it come to fees for bespoke services a good lawyer will subscribe to these principles:
Please bear in mind that the full details of the rules governing legal fees can be complicated, but as a general rule anything you agree to in advance (eg an hourly rate for example) is difficult to challenge afterwards, but other matters (eg number of hours spent) can be challenged.
Remember also that these rights usually only apply fully to clients. Others have more restricted rights and often no rights at all, because it is generally for the client to decide whether they are satisfied with the bill not anybody else. One particular exception to this is in probate where only the solicitors are the executors. In this event some beneficiaries also have rights to challenge the bill.