There is a lot to this question, and I will do my best to answer it for the period between 1603 and 1642 (with limited reach to the Elizabethan era), as that is the most relevant to the information presented in the question. There is much to say on taxation or the raising of funds in the medieval and Tudor periods, but I will let a proper medievalist give that information. Further, the question of how money was raised by James I and Charles I is directly related to one of the major questions in early modern English history: what caused the Civil Wars?

First, there are the terms. A "subsidy" is a specific amount of money to be drawn from the populace. It is not like an "income tax," where the item described is assessed and a certain dollar amount owed to the state. Parliaments in the Elizabethan and Early Stuart years spoke in terms of "subsidies," meaning that when the amount of one subsidy would not be enough, they would collect two or three subsidies. This happened, for example, in 1606 when James I was granted three subsidies by the sitting parliament. The assessment for a subsidy was 20% of the annual value of land held (4 shillings per pound sterling) OR 13.3% of the value of movable goods (2 shilling, 8 pence per pound sterling). The item of greater value was the one assessed, and no one was assessed against both his landed and movable wealth. (Dietz, English Public Finance, 1558-1641, pp. 381-382).

The other major form of parliamentary taxation was the "fifteenth and tenth," often shortened to just a "fifteenth". These were an older assessment than the subsidy, and the rate was initially fixed in 1334. The assessment for a "fifteenth" was a grant from the populace of 1/15 of the value of their movable property, if such property was held outside the "royal demesne" (meaning the crown was not the ultimate owner of the land). Those who did hold their land on the "royal demesne" were assessed at 1/10 their movable goods (Dietz, English Government Finance, 1485-1588, pp. 13-14). The value of a "fifteenth" was also substantially lower than that of a "subsidy," so they were more likely to be offered in multiple, if at all (Russell, Causes of the English Civil War, ch. 7).

Now, both of the above assessments (subsidy and fifteenth) were parliamentary taxes. That means they could not be collected without the initiation or approval of a parliament. Although modern taxes (in the US at least; income tax, sales tax, etc.), are perpetually collected, or collected as part of every transaction, a subsidy or a fifteenth had to be specifically offered and passed by a parliament. Thus, between the failure of the Parliament of 1629 and the meeting of the Short Parliament in 1640, there were no parliamentary taxes collected. This gets to the root of the problem; the disparity between the financial reality of the crown, and the theoretical obligations of the monarch imposed mainly by parliaments. Further, a parliamentary taxation was meant to be something issued in "extraordinary" circumstances; typically meaning rebellion or war. Without pressing military need, parliaments rarely granted subsidies or fifteenths.

James I and Charles I (and the Tudor monarchs before them) were expected by Parliament to "live of [their] own." The phrase, "to live of his own" meant that English Kings (and Queens) were expected to live on the money they earned from Crown lands, customs duties, and some remaining "feudal dues". I'm going to leave aside the questions associated with the term "feudal" and "feudalism," as they are far too intricate to work out here. For our purposes, "feudal dues" are sources of income drawn from the sale of wardships (when a person was too young to inherit property, the control and rents of the land reverted to the crown. The crown could then sell the right to collect rents and maintain the land, until the ward was old enough to inherit), licenses of widows to marry (another form of controlling the passage or inheritance of property), and the sale of escheated land (land that had been forfeited to the crown, either due to the death of the landholder without an heir, or as a result of the lands being forfeited to the crown because the owner had been convicted of a felony) (Baker, Introduction to English Legal History, 4th ed., p. 239; Dietz, Finance, 1558-1641, p. 303; Agrarian History of England & Wales, Vol. 4, p. 256).

Thus, English monarchs were expected to live within the budget outlined by these three sources of income (rents on land, customs, and feudal dues). The problem was that these funds were supposed to provide all the un-extrodinary income for the crown. So anyone collecting customs, the navy, the cost of ambassadors (both at home and abroad), the fees for crown servants, the cost of raising a royal family (which had to be done properly in order to maintain the respectability of the crown and country) were all expected to be drawn from this small amount of income. Both James I and Charles I found this impossible.

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