Provided it was a genuine connection (there are minimum transfers times at major stations) then yes, you are entitled to the delay in reaching your final destination, even on split tickets.

Email the company that incurred the initial delay.

I used to get lucky with this a lot coming back on East Coast on a Sunday, with an hourly connection at Peterborough. I'd always pop to the shops anyway to pick up something for tea, but a few minutes late and I'd be eligible for delay repay...