Update: For UK nationals post January 1. 2021.
In Spain that depends on where you park. In general, on parking places, reserved for disabled, you are exempt. In other areas (blue zones e.g.) each town has its own rules.
A survey of Spanish towns on the link below. It is best to inquire at town halls of towns you frequently visit, so as not be caught out by a fine if you need or wish to park outside of reserved parking spots.
Visitors to Spain using the Blue Badge from other EU Countries:
You may use your badge in all European Union and EEA countries. Please consider that the rules may vary so ask in each country you plan to visit. You may find this information at the tourist offices. Ask for examples of the notices for Blue Badge parking.
Note* The European blue badge from other countries are only valid when travelling. Once residing in a country different to where you card was issued, you should apply in your country of residence.