Yes. Indeed you can't hold a peerage and sit in the Commons.
This was famously a problem for Tony Benn, who was set to inherit his father's peerage. Because there was (back then) no way to surrender one!
The law had to be changed so he could do so, and this continue serving in the Commons.
Gods above, what a system 😂 (I'm joking. Democratic systems are good or bad depending on how well they works for the people using them, however they may look strange to someone outside)
Indeed no MONARCH has been allowed in the Commons, while its sitting, since the English Civil War in the 1600s.
Which was to a large part fought to make VERY clear to King Charles I who really ran things.