Most hotels in the UK do not ask for an ID when you check in, but I think I have been asked for one at times.
If you have your Spanish National ID card, bring that, if not bring your passport.
If you are not happy with taking your passport, call the hotel and ask whether they require it.
There is no border between England and Scotland and therefor you do not need to show a passport there.
Whether you need a passport in the train depends on your ticket. I do not know any train tickets in the UK where you need a passport, but there might some.
If you buy online and have a home print, you might need your passport or ID card, read the print on the ticket.