Just thought I'd add a post to this discussion being that we just went through a similar process of adding an infant born here in the UK to a Work Permit Visa.
We had inquired around about Immigration solicitor fees--and with a bit of searching--found ones that were about the same cost as the PEO fees listed above by WebyJ. Some offices were quite expensive, but even at the rate close to the PEO fees it was also comforting to know that someone was doing the paperwork properly.
However, I would note that the process took quite a long time. Perhaps because the terror alert went up? Certainly because the papers were in over the Christmas holidays. We submitted the papers at the end of November, and just got them back this week, 24 January.
Best,
Rutabega