The short answer is yes. Many people mistakenly- have been led to believe that because the property is in Spain, the Bank is in Spain and the mortgage debt is in Spain, that the Spanish Bank cannot come after them in the UK for the debt. This is certainly not the case.
In the majority of cases, the Bank in Spain will have a first charge on the property and are likely to attack that in the first instance. If they can sell the property through an auction process to cover the amount outstanding, then that would bring the matter to an end. However, if the value of the property is less than the amount outstanding then the Bank has a right to pursue a borrower for any shortfall.
For more information - https://www.judicaregroup.com/site/country/lawyers-in-spain/mortgage-problems-in-spain/spanish-bank-pursuing-assets-uk/