Health Insurance

I am hoping to move over full time in April with employment. Is it correct that that if I am working and paying tax, I do not need Private health insurance for me or my wife (who will not be working) we are both under retirement age.

Thanks in advance

Tom

Yes, it is correct. If you are on the system then part of your payments are for social security which covers your healthcare and just one person in the household paying it covers the other members of the family.
You will need a social security number (which your employers should apply for).

Some helpful guides on here:
Healthcare in Spain

Thanks Marcliffe