In theory they can but in practice it is not worthwhile unless you are talking about a sum in excess of €50k. Even then is is questionable.
They would first have to demonstrate that they have made all reasonable efforts to collect the money owed in the juristiction where the debt was incurred. At the very minimum this would entail getting a judgement against the creditor in a Spanish court first. They would then have to apply to both the English and Spanish courts to have the debt transferred. This is such an expensive and time consuming practice that it only ever happens when very large sums of money are involved.