Historically issuing of Letters of Marque and Reprisal started initially as a method of legal redress, the reprisal part hints at this. However this was so widely abused that it became little more than piracy. The diplomatic difficulties caused led states to agree on certain basic principles for the regulation of privateering.
Letters of marque were no longer used as a means of settling a private wrong and now were only issued at commencement of state sanctioned hostilities, that is following a declaration of war. That captured enemy vessels had to be judged before an Admiralty court and neutrals rights had to be respected. Infringement of these regulations could lead to the forfeiture of the bond for good behaviour or in some case the impressment of the offending crew.
The Second article in the Treaty of Ghent, which ended the war, included arrangements for prizes taken at sea:
Immediately after the ratifications of this Treaty by both parties.... to prevent all causes of complaint which might arise on account of the prizes which may be taken at sea after the said Ratifications of this Treaty, it is reciprocally agreed that all vessels and effects which may be taken after the space of twelve days from the said Ratifications upon all parts of the Coast of North America from the Latitude of twenty three degrees North to the Latitude of fifty degrees North, and as far Eastward in the Atlantic Ocean as the thirty sixth degree of West Longitude from the Meridian of Greenwich, shall be restored on each side:-that the time shall be thirty days in all other parts of the Atlantic Ocean North of the Equinoctial Line or Equator:-and the same time for the British and Irish Channels, for the Gulf of Mexico, and all parts of the West Indies:-forty days for the North Seas for the Baltic, and for all parts of the Mediterranean-sixty days for the Atlantic Ocean South of the Equator as far as the Latitude of the Cape of Good Hope.- ninety days for every other part of the world South of the Equator, and one hundred and twenty days for all other parts of the world without exception.
Prizes could still be legitimately taken up to, if my maths are correct, the 15/16 June 1815.
As to Acts covering the War itself the United States have been provided with a useful volume The Historical Register of the United States 53 mb, which gives the political background.
As far as I can determine Britain hasn't such a useful source and the various parliamentary proceedings have to be searched however the aforementioned Historical Register of the United States does include the diplomatic exchanges between governments.
If one delves into the various parliamentary proceedings of the period some curious cases can be found:-
House of Commons debates 25 Febuary 1812 c953
This case, on which he dwelt at considerable length, was shortly this: the privateer Daphne, belonging to a Mr. Jacob, in 1799 or 1800, captured the French vessel Circe, worth £30,000. which was condemned, and a claim to the contrary disregarded. The year and day for appeal having transpired, the condemnation became final, and £15,000. was shared among the captors. Ten thousand pounds more lay ready to be distributed.
At this point of time an information was laid against them for having disregarded the 33d of the King, by which a muster of the crew of a privateer before sailing is enacted. On the letter of this law they were convicted; the £10,000. stopped, and the £15,000. recovered, all of which had become Droits of Admiralty. The mere ignorance of the law was not admitted as an excuse: and the result to Mr. Jacob was costs to the amount of £1,700. and utter ruin. From having been in a respectable trade, be was thrown into goal, and reduced to poverty. It might be right for the House to be informed on what sort of authority it was that the money paid on account of the capture by the Daphne had been recalled, and Mr. Jacobs and his family reduced to beggary. It was not at the suggestion of a common informer, or of a qui tam attorney, but on evidence procured by a reverend clergyman—the Rev. W. B. Daniels, who had been in confinement for debt, and reduced to the condition of the primitive Christians, after publishing a work on Field Sports, in which he, as well as many of his brethren, were known so peculiarly to excel (hear, hear!) He did not mean to cast any general reflection on the numerous respectable members of the church of England; but certain it was that Mr. Daniels formed no addition to their respectability, for after other trades had failed, he turned a broker in evidence, and procured two men, of the names of Thatcher and Guzman, one of whom had been convicted of perjury, and the other had been flogged at the cart's tail, to swear as much as was necessary to support his charge. For this signal service, the worthy and reverend gentleman had received from government no less than £5,077. and the first of his witnesses £87. 13s. 7d. as a "gratuity for evidence given."
The works following show how complex the rules were and how careful the privateering commander had to be.
Henry J. Bourguignon, Sir William Scott, Lord Stowell: Judge of the High Court of Admiralty, 1798-1828 ( Cambridge University press, 1989
This gives and excellent academic survey of how prize law functioned in this period.
Richard Hill, The Prizes of war: the naval prize system in the Napoleonic Wars 1793 -1815 (UK:Sutton publishing, 1998)
Donald A. Petrie The Prize Game: lawful looting on the High Seas in the days for fighting sail (Maryland: Naval Institute press, 1999)
David J. Starkey British Privateering Enterprise in the Eighteenth Century (Exeter: University of Exeter, 1990)
This is an excellent work - as an example the PDF gives the first two chapters .