As it’s such an important topic, we feel it would be good to clarify this point further.
The simple answer is NO, you cannot ITV/MOT a British registered car in Spain. So if your vehicle was registered in the UK, you would have to have an MOT undertaken in the UK.
However, (and this can cause some confusion), you can take a UK registered vehicle to a Spanish ITV testing centre and request an inspection BUT, the inspection is considered to be voluntary and you will be issued with a report that states this at the top of the document.
This does NOT satisfy Spanish legal requirements! Under Spanish law this is NOT a valid ITV. A technical inspection certificate is only valid when done in the country in which the vehicle is registered.
A foreign vehicle can have a full and legal ITV in Spain only if it has been correctly imported and has been transferred to Spanish plates.
You are fully entitled to drive a UK registered car in Spain IF it is insured and has a valid MOT in the country in which it is registered, but only for a short period, i.e. you are on holiday or have just moved to the country.
If you intend to become a permanent resident, you must register the vehicle with the relevant authorities within 30 days of arrival. More information on importing a vehicle into Spain here.
Some people move to Spain with a UK registered car and think they can then drive it around continuously for months on end. You can, BUT if you are pulled over and it is determined that you are resident in the country and have not registered the vehicle you could face a fine and possibly have the vehicle crushed.
If the MOT has expired, you may also have invalidated any insurance policy you may have on the vehicle.