The issue that a non-resident will have in obtaining a lease agreement is in providing the standard rental requirements: 1) proof of current income, 2) prior current residence, 3) credit history, 4) social security, etc. The standard rental requirements in the United States are not easily obtained by a U.S. LL directly from the United Kingdom. (If supplied by tenant the information is not reliable, but at least verifiable.) There are methods to obtain and confirm foreign income and identity, but most LL's may not be familiar with the process. In such case, a willing LL may require first and last month’s rent, plus two month’s security (if allowed by law).
It will not be possible to secure a rental without employment, which requires a Working Visa, not a standard Visitor's Visa.