The UK is still a fully paid-up member of the EU so if you are planning to move to Spain permanently there is a very good argument to do so before we leave. Under international law, you will have been deemed to have acquired rights by simply being a resident in Spain and it is highly likely you will retain these rights once we leave.
While the host country is under no obligation to provide services such as healthcare, it is again likely that the UK will reach an agreement with other EU countries for a reciprocal arrangement as it would be in the best interests of the EU to look after their citizens given the millions of EU nationals living and working in the UK. If you’re buying a holiday home and not planning to live in Spain permanently then very little changes. Once the UK leaves the EU it would still be possible for Spain to impose additional or higher taxes on British owners, for example on a house sale, because the basic right for a Brit in the Costa del Sol to enjoy the same tax treatment as a Spanish national would have been lost.
What is unlikely however is that Spain would impose anything overly dramatic to deter British buyers, given we account for a substantial proportion of of Spanish property purchases by overseas buyers. So far, it’s good news for British pensioners looking to buy in Spain. A deal has been made in principle which will allow pensioners to retain usage of the European Health Insurance Card (EHIC) whilst living overseas, and there has been progress on the transfers of pensions too. Adding to this, in October 2017 Spain’s foreign minister Alfonso Dastis pledged that individuals who purchase in Spain will face no disruption once Britain leaves the EU and that the relationship between the UK & Spain is a very close one in terms of economic and social exchanges.