I'm in the Civil Defence and our first aid training is of a really high standard. In the Casualty units they can train you right up to EMT level which would stand you in good stead to go forward for paramedic training. It's all PHEEC approved and to their standard.
If you fancied going down that route, contact your local CD unit but be sure and go for a "Casualty" unit. While all CD volunteers get First Aid training a casualty unit would probably cover it all quicker as it's their speciality.
In truth, the Red Cross or similar might be better for you. Civil Defence however has a very varied and interesting role to play these days.