Hi Rach and welcome to the forum!
By far the easiest way to get a caving experience for you and your boyfriend is to engage the professional services of an instructor:http://www.caveinstructor.org.uk/instructors
They will provide all the necessary equipment, leadership/guidance, insurances, expertise, knowledge and experience to make a great introductory day out.
If you love it, you can then look to getting your own gear and joining a club you find suits you.
If you want to get underground quick, on your own terms, with the trip dedicated to you and tailored to you, then this is THE more effective and simple way to do it. Obviously it will involve expense though.