How many British monarchs have abdicated?

It depends what you mean by abdicated. Only one renounced the title of king of his own volition, Edward VIII, but there were others like Chas I, Richard II and Edward II who were deposed - forced off the throne by others.

Richard II and Edward II were forced to abdicate, James II was deemed to have abdicated and Edward VIII voluntarily abdicated.

Edward VIII was indeed a famous one, abdicating in 1936 after 325 days on the throne, choosing to marry someone that would not have been allowed by the Church of England he was meant to be the head of.

Beside Edward VIII, I found three examples from the UK:
Edward II in 1327, Richard II in 1399, and James II/VII in 1688
All were forced to abdicate under duress due to coups or an invading army.

Looking further afield, Dermot McMurrough abdicated from Leinster (a region of south-east Ireland) in 1169. And even further, there are dozens of examples of abdications in global history.

https://en.wikipedia.org/wiki/List_of_monarchs_who_abdicated