The deadline for euro-denominated payments in non-euro area countries will be 31 October 2016.1
The IBAN only rule is part of the SEPA regulations outlined in European Regulation 260/2012. It includes several key dates. The February 1 deadline for IBAN-only transactions only applies to euro countries because non-euro countries are specifically exempt from the other deadlines:
As the European Payments Council (EPC) explains
In non-euro countries, the deadline will be 31 October 2016. Effectively, this means that as of these dates, existing national euro credit transfer and direct debit schemes will be replaced by SEPA Credit Transfer (SCT) and SEPA Direct Debit (SDD).
The ECB site confirms that date.
Note that SEPA regulations apply only to payments made in Euro currency.
Experian has a handy countdown timer and summarises UK banks' responsibilities:
For the majority of the Eurozone, domestic SEPA (Single Euro Payments Area) became a reality by August 2014. For those Euro bank accounts not held in the Eurozone, SEPA deadlines are due to be enforced from October 2016
From October 2016, changes are being introduced that will affect all SEPA payments from UK accounts, including cross-border. Until then, SEPA payment instructions require payers to include a BIC (Bank Identifier Code). From October, banks must accept payment instructions containing only IBANs.
1 - European Central Bank, Migrating to the Single Euro Payments Area: key facts