AFAIK you don’t own the shares - from their T&C
8.1 Investments that you buy or subscribe for or transfer into your Interactive Investor Account will be held in Safe Custody in your Interactive Investor Account (either in the Nominee or to its order) in accordance with the following arrangements (or such other arrangements as we may notify you of on our Website from time to time).
Most Investments that you buy or subscribe for or transfer into your Interactive Investor Account, such as shares traded on a UK Exchange, will be held in Safe Custody in the Nominee itself. Under this arrangement, the Nominee has legal title to the relevant Investments and you retain the beneficial entitlement at all times.
The explanation of the “Nominee” is given in the preamble
means Investor Nominees Limited, the nominee company owned by us and in whose name certain of your Investments will be registered or held to its order, or any successor or alternative nominee company we may appoint from time to time
Basically the shares are held for you but title to them does not pass to you.
What you can do, of course is sell the holding back to iii, withdraw the cash and buy the shares back with another broker - this isn’t ideal as you will loose out on the dealing spread and you might need to watch the timing so as not to loose dividend payments.