It is very hard to say since like all wealthy people they had excellent accountants who minimised their taxes as much as possible. But what the song taxman is referring to is the high marginal tax rate that Britain had at the time which was 83% on income over a certain amount. However that is not only what the song is referring to, it is mostly referring to the surtax. This tax was an additional tax on very high earners that took their highest bracket to around 95%.

However whilst this number seems very high by the time Taxman came out in 1966 the Beatles were no longer paying that amount. Like today capital gains were taxed at the much lower rate of 30%. So Lennon and McCartney founded Northern Songs which went on the Stockmarket and thus allowed them to avoid the high tax rate and soon after that Harrison founded Harrissongs and Starr founded Startling Music for the same purpose as well as some other reasons to better promote their songs.

To add another question: how much tax were the Kinks paying when they wrote "Sunny Afternoon"? Should be similar. Both were in England around time.