Modern countries vary widely in how much they tax their citizens (https://en.wikipedia.org/wiki/List_of_countries_by_tax_revenue_as_percentage_of_GDP). Where do historical monarchies fit into this spectrum? For example, what proportion of GDP was taken in tax under Henry VIII? How does the Roman empire compare? Is there wide variation between countries and over time?
GDP is a purely modern concept; it was proposed by Simon Kuznets in the early 1930s. All GDP statistics for earlier times are retrospective estimates, growing more uncertain the further back into the past the estimate goes. For pre-modern times, we are pretty much left with rough guesses based on estimates for population size and consumption per person, a few scattered statistics on icome and prices, as well as - indeed - tax revenues.
Also note that (besides conceptual problems) there are many things not accounted for in the GDP, the informal economy, housework, etc. The share captured by the GDP differs between countries today (especially between developed countries and developing countries) and this would hold even more strongly compared to earlier times.
Pre-modern taxation systems tended to be simpler than the ones we have today; mainly because it is important that taxpayers understand what they have to pay and tax collectors know how much they have to collect (both were not generally very sophicticated or well-educated people). Popular were for instance rules of thumb - like a tax rate of one tenth (see the word tithe): if you were not good in maths, you could just use your 10 fingers to count how much tax you had to pay, 9 for you and 1 for the tax collector. As the wikipedia article on tithe describes, it was used widely across time and regions from the ancient near east to pre-modern India to the middle ages in England. Of course, the way it was collocted differed from today, it was not so much an income tax (impractical with low population density) as a market tax (an early form of VAT if you will); if public finances would run low, the authorities would get creative, however, and introduce new taxes on the most absurd things, beards (Henry VIII of England and Peter I of Russia), coffee (France), windows (England and Wales) and curtains (Denmark, if I remember correctly). Early forms of income tax would estimate not your income but the value of your family home/estate (e.g. in the Netherlands), i.e. being closer to a property tax. Note that governments have a number of other ways to improve their finances, e.g. by debasing the currency or by defaulting on their public debt. Both has become rather unpopular in recent decades but was very very common in pre-modern and early modern states. Note that inflation (by debasing the currency) acts economically also like a tax.
Forced labor would also be closely retaled to taxes in pre-modern and early modern systems. Some link this to the very emergence of money, but in any case armies (and the Royal Navy in early modern times) would capture unsuspecting civilians and force them into service; rich people would have been able to buy their way out of this.
From this, you could potentially deduce - as a first approximation - a tax rate of around 10 percent. Note, however, that goods would likely be taxed as often as they would be sold (modern VAT is only applied once). Together with taxes for windows, coffee, beards, etc etc. this would in most cases probably yield a much higher effective tax rate. Also, corruption would have been rampant and very little of the collected taxes would arrive at the king's court (or whereever they should legally go); in fact, in Roman times, it was a commonly accepted fact that senior officials would conclude their carreer as provincial governors embezzling huge sums from the local economy. Does it still count as taxes compared to the GDP? Further, tax rates and efficiency of tax systems (even beyond corruption) differed widely. Note that the very definition of taxes also changed over time. Over longer periods, (the descendants of) tax collectors may for instance become feudal landlords and landowners - what they did, did not change, they continued to collect whatever revenue they could from the farmers etc under their control. (That pretty much describes the transition from Roman antiquity to the European middle age.)
England under Henry VIII
Now to your original question: the tax rate under Henry III of England - see here, the goods tax was 2s 8d on the pound, other taxes existed as well, that gives perhaps around 20%. Note, however, the obvious failure of the taxation system: they regularly raised only about a third of the projected tax revenues.