Using iPad abroad

Check with the front desk. More than likely they use a sign-in page for the wi-fi and you just have to do that. This support document explains how captive wi-fi networks work, and it sounds like that is what your hotel has. Use captive Wi-Fi networks on your iPhone, iPad, or iPod touch - Apple Support

I would also be willing to guess that you are not the only iPad user that has had issues with connecting to their wi-fi. If you ask them at the front desk, they will probably assist you in getting it connected.

So the iPad works in the UK, and in one hotel in PT, but not in another PT hotel?

That implies a problem with network access with one PT hotel, not with the iPad.

Connecting to the Wi-Fi router is just part of what’s involved with accessing the ‘net.

Try some other PT-area Wi-Fi networks. See what happens on those.

It probably picked up information from your iPhone. However, it still may have needed to use the captive network sign-in on the iPad itself. Try opening up Safari on the iPad and then type in the hotel's website address. If that does not do it, then stop by the front desk.