Alimony is not 'earned income'; earned income is quite literally 'earned' e.g. from employment.
Also, make sure you understand this paragraph from Article 17 of the US-UK tax treaty if it applies to you:
Periodic payments, made pursuant to a written separation agreement or a decree of divorce, separate maintenance, or compulsory support, including payments for the support of a child, paid by a resident of a Contracting State to a resident of the other Contracting State, shall be exempt from tax in both Contracting States, except that, if the payer is entitled to relief from tax for such payments in the first-mentioned State, such payments shall be taxable only in the other State.