Yes, you will need to go through probate and also probably as part of that get a tax clearance certificate on your fathers affairs. If all he had was a state pension and no savings or investments, that should be straightforward enough.
End to end and depending on where you live in the country, it could take ballpark a year to be completed.
The information in the above link should help inform the OP about the process, and whether they feel they can or should do it themselves as a personal applicant.
Having been a personal applicant myself in the past I would recommend it whilst acknowledging that it isn't for everyone either.