I hate to add another nay-sayer to the chorus, but here it is:
Do NOT try to live here on a visitor's stamp. If you are caught, you will be out-and-out banned from entering the UK for any reason, for quite some time--three years is typical.
I am quite familiar with people who have tried this strategy, as it is one of the things gays sometimes resort to in order to build up the two years' cohabitation necessary for us to get an Unmarried Partner visa and live here properly. (I hasten to say that I did NOT do this myself, on the advice of my immigration lawyer who informed me that I would most likely get away with the first visitor's entry, and possibly the second, but on the third I had a 99% likelihood of being detained, questioned, deported and banned. I came here legally as a student, and it worked out well because I got to learn a new skill while building up time towards my partner visa.)
Please understand that if you are banned from the UK for immigration violations, they can make it difficult for you to get in later even if you otherwise would qualify--if you had a valid offer of work, if you married a Brit or any other legal basis for entry. Basically, you would be on the bad list. You do not want to be on HM Immigration's bad list, believe me.
Also, you cannot get citizenship by simply visiting over a four year period. You have to live here as an "ordinary resident" for five years (reduced to 3 if your spouse or partner is British), and at least one of those years MUST be on "Indefinite Leave to Remain," which is the UK equivalent of the US green card. The only way into the ILR, and thus the citizenship pipeline, is by getting the proper visa first. Even I must wait an additional two years because my first 2 years here as a student don't count as "ordinary residence" for the purpose of citizenship. And I was here legally, not trying to fudge a visitor's visa into long-term residence.
I suggest you see if you qualify for the Highly Skilled Migrant Programme, or for the special self-employed artist/writer visa. The latter requires significant finances, but it's worth a look.
Sorry to be such a downer.