Using UK passport to freely travel in EU

The UK formally leaves the EU at the end of March 2019. But does this mean that from that date forwards, we cannot use the UK passport to travel across EU countries freely, as is the case now? I tried to find this out, but got nowhere and the problem is that the UK leaves the EU in stages. At which of these stages is the UK passport not valid to travel across the EU freely?

Nothing is confirmed as of now. Probably an Online form and a small fees (10 Euros) will give prior authorization before entering EU. Similar to what British Passport holders need to do before going to USA, Canada. ESTA for travel. For any long term stay, visa might be required.

What's running through my mind. My mother was born in Ireland and it should be quite easy for me to get an Irish passport. This passport will allow me to continue to travel across EU countries with no hassle. But I ask myself if I need to take the step of applying now for the Irish passport if I can still use my UK passport for a time after March 2019 to continue to travel freely across EU countries.

Maybe it's worth applying now - when the crunch comes (i.e. people realising the gravity of the situation) then you are ahead of the curve.

Luck favours the prepared