I work for the Export Control Organisation, part of the Department for Business, Innovation and Skills (BIS). ECO is the UK's export licensing authority for military and dual-use goods.
Guidance about export controls is now published on https://www.gov.uk.
This includes the latest position concerning sanctions imposed by the international community on Iran - see the guidance published at: https://www.gov.uk/sanctions-on-iran and you should read this carefully as the prohibitions on Iran are very extensive.
If the items you are exporting (ie TFT monitors) are commercial, off-the-shelf products and have not been specially designed or modified for military use then these items will not be listed on either the UK Strategic Export Control Lists or in specific sanctions lists and hence controlled for export purposes.
If however the items are modified in some way (eg plug is changed to military specification) then the item will be listed and hence controlled and require a licence.
If the items are not listed on the Control Lists you do also need to be aware of end-use controls - see https://www.gov.uk/weapons-of-mass-destruction-wmd-end-use-control and
The ECO operates an "End-User Advice Service" where you can seek advice on the end-user company you are intending to export to. This advice needs to be requested online via the ECO's SPIRE export licensing database - https://www.spire.bis.gov.uk
Mike Barnes, who responded earlier, is also totally correct in saying that even if the goods are not controlled (either because they are listed or on the grounds of end-use), that you need to check the position about exporting to Iran with your bank. Their are financial restrictions for banks, credit and other financial institutions which prohibits all financial transactions and business relationships between UK financial and credit institutions and banks incorporated in Iran.