Questions about being barred from entry into the UK 10 years down the road need to be asked some number of years in the future. Current practice is that the Home Secretary does not bar entry because of an unpaid debt, instead you have to do something egregiously bad or antisocial. Given Brexit, future matters of immigration are not set in stone.
One consequence of walking away from a lease is that you are likely to be sued (in UK courts) for breach of contract, and the court may find that you owe the rest of the lease money. If that happens, you need to be concerned with whether the judgment can be enforced against you, even when you are in the US. The general answer is, yes, the landlord can petition the US courts to enforce a UK judgment against you. The specific details depend on the law of your state, but most states have a version of the Uniform Foreign Money Judgments Recognition Act. In addition, the landlord could sue you in US courts (maybe not as convenient for him). There is no requirement that you have to be a US citizen to sue a US person, and a landlord can (would almost certainly) sue you via a US attorney who would represent him.
An alternative to fleeing your obligation and saying "Go ahead and sue me!" is to negotiate a termination of the lease. The landlord would have a duty to mitigate his losses, so if the remainder of the lease has a value of $2,000 a month for 8 months, the landlord can't just do nothing -- he has to try to rent the unit out, so perhaps his actual losses would be only $4,000. Suing a person is expensive especially when you you are dealing in trans-national disputes, so he may be willing to accept some figure in exchange for terminating the lease. Your (UK) lawyer will give you good advice on how to proceed, if you opt to not get sued.
