No I cannot afford to trace my family tree.
Yes archives in the UK go back that far but most families can only trace their family back to about 1860-1880 when social institutions like churches and charities began keeping records.
A few can trace back their ancestry to the 1700's some more lucky ones can trace their ancestry back further. But it is not easy for most people, it involves a lot of work and money and years of searching. Unless you are very rich, the wealthy families tend to keep their records intact.
Also it is very easy to make mistakes if you are not an expert in old records to make mistakes and follow the wrong line. The BBC who has access to experts and lots of money have often; had to abandon some celebrity programs when their family tree was uninteresting. And did not fit into the particular topic they wanted the program to reflect. Such as
Grandparents were slaves or a slave trader.
Grandparents were jewish and changed surname to English.
Grandparents were polish refugees.
Grandparents were social reformers
Grandparents were extremely poor.
Grandparents fought bravely in a battle or war.
Grandparents were on the pilgrim ships to America.
Grandparents were Quakers or Puritans many who went to America.
Each program is particularly trying to show or indirectly teach about an aspect of UK history.
All records are open and available to look at online, there may be a charge in some cases and to follow each link will cost a great deal of money.