I believe you have established a good relationship with your clients. Personally I will simply ask for what I want. A lot of problem can be solved by good communication. Try to put yourself on their shoes and point out the benefits they have to work with you in a freelancing way.
That's right, with 7 years of experience, you should charge at least £20 an hour. By working as self-employed, you don't have paid holidays, sick leave or any other benefits.
Though, I suggest you to increase your charge gradually as [(20-16)*100% = 20%] 20% pay rise may sounds alot at the first place.
