Hi Jonathan – this is from the horses mouth!
1. From Spain go to the UK Embassy web site and find form C1, which is specific to applications for ex-pats in Spain
2. The application form is for a new initial passport
3. You need a letter from your employer (on headed paper) explaining why you need an additional passport (i.e. visiting confliciting countries)
4. 2 pictures one of which needs to be ceritfied
5. Your current passport needs to be sent in with the application unless it is being used in which case your employer needs to explain in the letter why your passport is not available.
6. If you cant send your passport you need to send an original full birth certificate in lieu of your passport
I hope that this information is useful and it enables you to achieve your objectives.
Any further help, please do not hesitate to contact me.
Have a good weekend