The matter of whether you were travelling on a through ticket or two point to point tickets would also come into play (at least as far as the UK is concerned.)' If using two separate tickets, the company concerned would no doubt argue that while they regret the delay to your flight, they had fulfilled the terms of the contract by delivering you to the stated destination and that their liability stops at that point.
As Dave Reid correctly points out, the incident described could most certainly only properly be described as a tech delay.