Hmm, I noticed that the 'On the House' Origin page does not mention Securom:
https://www.origin.com/en-gb/store/on-the-house-ANW.html INTERNET CONNECTION, ORIGIN ACCOUNT, ACCEPTANCE OF PRODUCT AND ORIGIN END USER LICENSE AGREEMENTS (EULAS), AND INSTALLATION OF THE ORIGIN CLIENT SOFTWARE (WWW.ORIGIN.COM/ABOUT) REQUIRED TO PLAY. YOU MUST BE 13+ TO ACCESS ONLINE SERVICES AND FEATURES. EA ONLINE PRIVACY POLICY AND TERMS OF SERVICE CAN BE FOUND AT WWW.EA.COM. PLEASE REVIEW EULAS AND ADDITIONAL IMPORTANT DISCLOSURES APPLICABLE TO SPECIFIC PRODUCTS AT WWW.EA.COM/1/PRODUCT-EULAS. ONLINE FEATURES AND SERVICES ARE NOT GUARANTEED. EA MAY RETIRE ONLINE FEATURES AND SERVICES (IF ANY) AFTER 30 DAYS NOTICE POSTED ON WWW.EA.COM/1/SERVICE-UPDATES. EA MAY PROVIDE CERTAIN INCREMENTAL CONTENT AND/OR UPDATES FOR NO ADDITIONAL CHARGE, IF AND WHEN AVAILABLE.
But the Dead Space page does:
https://www.origin.com/en-gb/store/buy/dead-space/pc-download/base-game/standard-edition-ANW.html INTERNET CONNECTION, ONLINE AUTHENTICATION AND ACCEPTANCE OF END USER LICENSE AGREEMENT REQUIRED TO PLAY. THIS PRODUCT INCLUDES SECUROM COPY PROTECTION TECHNOLOGY FROM SONY DADC. FOR MORE INFORMATION, INCLUDING HOW TO UNINSTALL SECUROM, VISIT WWW.SECUROM.COM.
Oh well, Securom is not getting onto my machine.