You can easily find out an available extension in Magento Connect which integrates Barclays ePDQ payment method for Magento. However, as Barclays no more supports this so the module is outdated. It is said to be compatible with Magento 1.1 but I am sure that nobody uses that version now. In my last project, I have to implement this payment for Magento 1.7 and luckily, I can still find good information around the world. Support team from Barclays also sent a good document for implemtation and debugging.
You can find the old version here: http://www.magentocommerce.com/magento-connect/barclays-epdq.html
I made some changes for the module to work with Magento 1.7, tested and implemented into the live site. Here you can download it.
You can also try to have a look at integration document which can help you something.
If you have any problem, don't hesitate to ask us.