I have not definitively been able to determine if there were laws on the books of the US or of England, between years 1600-1800, that restricted "free men" from working in any profession that they were competent for such positions.
Laws restricting who could be an attorney, even if they could pass the Bar exam of the time (which were oral analysis to measure their understanding), are the most sought after, but other professions outside of farming are highly desired as well (Blacksmiths, Bakers, Barbers, Hat makers, shoemakers, etc...).
I clarify "free men" since at the time slaves, women, and when children would be given to a "Master" to learn certain skill sets for a determined number of years, couldn't make their own decision. I'm also not inquiring into positions of governmental officials.
They were typically locally restriced in a mastership fee ( towns (town citizenships, property ownership, credit, but again, with differences between cities and periods ... ), guild memberships (although this also needs closer inspection as it varied, and the decline during early modern period, and of course between different occupations and regulations pertaining to specialised activities, with finished apprenticeship or otherwise qualified and demonstrated competences ), and of course product restrictions ( not technically work, but patents and monopolies on products might substantially hinder one´s ability to work, like, trivially, Stationers’ Company monopoly in printing even into the eighteenth century ).
With all of those taken into account, mastership quotas as such were typically absent in Britain by themselves ( and some other territories, like France etc. ), which seems to be the question here. Yet not to be confused with apprenticeship quotas, which still happened.
In terms of legal profession, the issue is likewise nuanced, the shifting differences and requirements between attorneys, solicitors and barristers throughout early modern period, their respective relation to the bar and jurisdiction, without going into details here.^(1) Local courts in this respect were notably different in early modern period ( as to the Westminster courts in general ), as attorneyships were a subject of local town governing bodies, and were sometimes increasingly prohibited or limited that attorneys of local courts should practice law at Westminster so as to serve local needs, Ipswich being one example. As to the matter of appointment, Canterbury in 1656 (p.42) specified that only the local clerk, recorder and attorney has the privilege to instruct for eligibility of attorneyship, other towns ( and other similiar jurisdictions ) were quite similar in these basic regards, so these provincial offices and activities have substantially different criteria than "higher" courts of London and Inns. One example (p.45) has it that attorney of Common Pleas was not allowed to represent a client in a manorial courts in 1686, and after adjuornment the case was dropped. Point being that in early modern period there was no single and universal qualification to practice within different jurisdictions ( as both a matter of territory and different kinds of courts, whose recognition was needed ).