First of all, you have to figure out what you did wrong in immigration process that they denied your case.
- Did you overstay on visa waiver program?
- Did you overstay tourist visa?
- Any criminal backgrounds?
- Insufficient income on the sponsor's part... if it is in this case, you can have joint sponsor.
If you have 1-3, then you should consider having immigration attorney to handle your case. Normally it is much easier for US citizen to obtain British citizen, especially on family based. You don't even have to take the "Life in UK Test".
Get this done first, renunciation of US citizenship is not the key to your answer.