I am pretty sure NJE accepts all JAA licences but if they ask you to change it it is to ease the admin work and reduce the time to do it when going for type ratings, renewals etc... NJE will hire you on the basis of your Spanish licence but if they feel it could be a good idea for you to get a UK one, they will tell you and pay all the costs.
That will include licence fee and an airline ticket to LGW so you can drop off and pick up your licence.
I am not sure about Spain but France, Italy can be real pains to get the type rating put on it. Weeks if not months... In the UK, you will drop it off at the CAA in the morning before 11 and pick it up by 1500. In my case, I wouldn't go for the french system as anything to do with French admins drives me crazy.
When you go to the interview, it is very likely that the HR person will explain that to you. It won't be a surprise when you join NJE so you will have time to think about whether or not changing your licence against getting a job at NJE, is a wortwhile option.